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<div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Measurements and equations</span> </div> </a> <button aria-controls="toc-Measurements_and_equations-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Measurements and equations subsection</span> </button> <ul id="toc-Measurements_and_equations-sublist" class="vector-toc-list"> <li id="toc-Volume" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Volume"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Volume</span> </div> </a> <ul id="toc-Volume-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Center_of_mass" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Center_of_mass"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Center of mass</span> </div> </a> <ul id="toc-Center_of_mass-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Right_circular_cone" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Right_circular_cone"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Right circular cone</span> </div> </a> <ul id="toc-Right_circular_cone-sublist" class="vector-toc-list"> <li id="toc-Volume_2" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Volume_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3.1</span> <span>Volume</span> </div> </a> <ul id="toc-Volume_2-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Slant_height" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Slant_height"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3.2</span> <span>Slant height</span> </div> </a> <ul id="toc-Slant_height-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Surface_area" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Surface_area"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3.3</span> <span>Surface area</span> </div> </a> <ul id="toc-Surface_area-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Circular_sector" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Circular_sector"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3.4</span> <span>Circular sector</span> </div> </a> <ul id="toc-Circular_sector-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Equation_form" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Equation_form"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3.5</span> <span>Equation form</span> </div> </a> <ul id="toc-Equation_form-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Elliptic_cone" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Elliptic_cone"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Elliptic cone</span> </div> </a> <ul id="toc-Elliptic_cone-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Projective_geometry" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Projective_geometry"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Projective geometry</span> </div> </a> <ul id="toc-Projective_geometry-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Generalizations" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Generalizations"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Generalizations</span> </div> </a> <ul id="toc-Generalizations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Cone</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 103 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-103" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">103 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Ke%C3%ABl" title="Keël – Afrikaans" lang="af" hreflang="af" data-title="Keël" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%88%BE%E1%8C%A3%E1%8C%A3" title="ሾጣጣ – Amharic" lang="am" hreflang="am" data-title="ሾጣጣ" data-language-autonym="አማርኛ" data-language-local-name="Amharic" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%AE%D8%B1%D9%88%D8%B7" title="مخروط – Arabic" lang="ar" hreflang="ar" data-title="مخروط" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-hyw mw-list-item"><a href="https://hyw.wikipedia.org/wiki/%D5%94%D5%B8%D5%B6" title="Քոն – Western Armenian" lang="hyw" hreflang="hyw" data-title="Քոն" data-language-autonym="Արեւմտահայերէն" data-language-local-name="Western Armenian" class="interlanguage-link-target"><span>Արեւմտահայերէն</span></a></li><li class="interlanguage-link interwiki-ay mw-list-item"><a href="https://ay.wikipedia.org/wiki/Pullu" title="Pullu – Aymara" lang="ay" hreflang="ay" data-title="Pullu" data-language-autonym="Aymar aru" data-language-local-name="Aymara" class="interlanguage-link-target"><span>Aymar aru</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Konus" title="Konus – Azerbaijani" lang="az" hreflang="az" data-title="Konus" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%DA%A9%D9%88%D9%86%D9%88%D8%B3" title="کونوس – South Azerbaijani" lang="azb" hreflang="azb" data-title="کونوس" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ban mw-list-item"><a href="https://ban.wikipedia.org/wiki/Kojong" title="Kojong – Balinese" lang="ban" hreflang="ban" data-title="Kojong" data-language-autonym="Basa Bali" data-language-local-name="Balinese" class="interlanguage-link-target"><span>Basa Bali</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%83%D1%81" title="Конус – Belarusian" lang="be" hreflang="be" data-title="Конус" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%83%D1%81" title="Конус – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Конус" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%83%D1%81" title="Конус – Bulgarian" lang="bg" hreflang="bg" data-title="Конус" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Kupa_(geometrija)" title="Kupa (geometrija) – Bosnian" lang="bs" hreflang="bs" data-title="Kupa (geometrija)" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Con" title="Con – Catalan" lang="ca" hreflang="ca" data-title="Con" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%83%D1%81" title="Конус – Chuvash" lang="cv" hreflang="cv" data-title="Конус" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Ku%C5%BEel" title="Kužel – Czech" lang="cs" hreflang="cs" data-title="Kužel" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Charaka" title="Charaka – Shona" lang="sn" hreflang="sn" data-title="Charaka" data-language-autonym="ChiShona" data-language-local-name="Shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/C%C3%B4n" title="Côn – Welsh" lang="cy" hreflang="cy" data-title="Côn" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Kegle_(geometri)" title="Kegle (geometri) – Danish" lang="da" hreflang="da" data-title="Kegle (geometri)" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Kegel_(Geometrie)" title="Kegel (Geometrie) – German" lang="de" hreflang="de" data-title="Kegel (Geometrie)" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Koonus" title="Koonus – Estonian" lang="et" hreflang="et" data-title="Koonus" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9A%CF%8E%CE%BD%CE%BF%CF%82" title="Κώνος – Greek" lang="el" hreflang="el" data-title="Κώνος" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Cono_(geometr%C3%ADa)" title="Cono (geometría) – Spanish" lang="es" hreflang="es" data-title="Cono (geometría)" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Konuso" title="Konuso – Esperanto" lang="eo" hreflang="eo" data-title="Konuso" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Kono" title="Kono – Basque" lang="eu" hreflang="eu" data-title="Kono" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%AE%D8%B1%D9%88%D8%B7" title="مخروط – Persian" lang="fa" hreflang="fa" data-title="مخروط" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/C%C3%B4ne_(g%C3%A9om%C3%A9trie)" title="Cône (géométrie) – French" lang="fr" hreflang="fr" data-title="Cône (géométrie)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/C%C3%B3n" title="Cón – Irish" lang="ga" hreflang="ga" data-title="Cón" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Cono" title="Cono – Galician" lang="gl" hreflang="gl" data-title="Cono" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E9%8C%90%E5%BD%A2" title="錐形 – Gan" lang="gan" hreflang="gan" data-title="錐形" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%B6%E0%AA%82%E0%AA%95%E0%AB%81" title="શંકુ – Gujarati" lang="gu" hreflang="gu" data-title="શંકુ" data-language-autonym="ગુજરાતી" data-language-local-name="Gujarati" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9B%90%EB%BF%94" title="원뿔 – Korean" lang="ko" hreflang="ko" data-title="원뿔" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BF%D5%B8%D5%B6" title="Կոն – Armenian" lang="hy" hreflang="hy" data-title="Կոն" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B6%E0%A4%82%E0%A4%95%E0%A5%81" title="शंकु – Hindi" lang="hi" hreflang="hi" data-title="शंकु" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Sto%C5%BEac" title="Stožac – Croatian" lang="hr" hreflang="hr" data-title="Stožac" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Kerucut" title="Kerucut – Indonesian" lang="id" hreflang="id" data-title="Kerucut" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Cono_(geometria)" title="Cono (geometria) – Interlingua" lang="ia" hreflang="ia" data-title="Cono (geometria)" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Keila_(r%C3%BAmfr%C3%A6%C3%B0i)" title="Keila (rúmfræði) – Icelandic" lang="is" hreflang="is" data-title="Keila (rúmfræði)" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Cono" title="Cono – Italian" lang="it" hreflang="it" data-title="Cono" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%97%D7%A8%D7%95%D7%98" title="חרוט – Hebrew" lang="he" hreflang="he" data-title="חרוט" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Pasungan" title="Pasungan – Javanese" lang="jv" hreflang="jv" data-title="Pasungan" data-language-autonym="Jawa" data-language-local-name="Javanese" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%B6%E0%B2%82%E0%B2%95%E0%B3%81" title="ಶಂಕು – Kannada" lang="kn" hreflang="kn" data-title="ಶಂಕು" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%99%E1%83%9D%E1%83%9C%E1%83%A3%E1%83%A1%E1%83%98" title="კონუსი – Georgian" lang="ka" hreflang="ka" data-title="კონუსი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%83%D1%81" title="Конус – Kazakh" lang="kk" hreflang="kk" data-title="Конус" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Pia" title="Pia – Swahili" lang="sw" hreflang="sw" data-title="Pia" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Konik" title="Konik – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Konik" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%83%D1%81" title="Конус – Kyrgyz" lang="ky" hreflang="ky" data-title="Конус" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Conus" title="Conus – Latin" lang="la" hreflang="la" data-title="Conus" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Konuss" title="Konuss – Latvian" lang="lv" hreflang="lv" data-title="Konuss" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/K%C5%ABgis" title="Kūgis – Lithuanian" lang="lt" hreflang="lt" data-title="Kūgis" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Cono" title="Cono – Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Cono" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/K%C3%BAp" title="Kúp – Hungarian" lang="hu" hreflang="hu" data-title="Kúp" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%83%D1%81" title="Конус – Macedonian" lang="mk" hreflang="mk" data-title="Конус" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Kitsoloha" title="Kitsoloha – Malagasy" lang="mg" hreflang="mg" data-title="Kitsoloha" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B5%E0%B5%83%E0%B4%A4%E0%B5%8D%E0%B4%A4%E0%B4%B8%E0%B5%8D%E0%B4%A4%E0%B5%82%E0%B4%AA%E0%B4%BF%E0%B4%95" title="വൃത്തസ്തൂപിക – Malayalam" lang="ml" hreflang="ml" data-title="വൃത്തസ്തൂപിക" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Kon" title="Kon – Malay" lang="ms" hreflang="ms" data-title="Kon" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mdf mw-list-item"><a href="https://mdf.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%83%D1%81%D1%81%D1%8C" title="Конуссь – Moksha" lang="mdf" hreflang="mdf" data-title="Конуссь" data-language-autonym="Мокшень" data-language-local-name="Moksha" class="interlanguage-link-target"><span>Мокшень</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%83%D1%81" title="Конус – Mongolian" lang="mn" hreflang="mn" data-title="Конус" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Kegel_(ruimtelijke_figuur)" title="Kegel (ruimtelijke figuur) – Dutch" lang="nl" hreflang="nl" data-title="Kegel (ruimtelijke figuur)" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%86%86%E9%8C%90" title="円錐 – Japanese" lang="ja" hreflang="ja" data-title="円錐" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Keegel" title="Keegel – Northern Frisian" lang="frr" hreflang="frr" data-title="Keegel" data-language-autonym="Nordfriisk" data-language-local-name="Northern Frisian" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Kjegle" title="Kjegle – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Kjegle" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Kjegle" title="Kjegle – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Kjegle" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/C%C3%B2n" title="Còn – Occitan" lang="oc" hreflang="oc" data-title="Còn" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Biilalee_(Koonii)" title="Biilalee (Koonii) – Oromo" lang="om" hreflang="om" data-title="Biilalee (Koonii)" data-language-autonym="Oromoo" data-language-local-name="Oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Konus" title="Konus – Uzbek" lang="uz" hreflang="uz" data-title="Konus" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%A8%D9%88%DA%A9%D8%B1" title="بوکر – Pashto" lang="ps" hreflang="ps" data-title="بوکر" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%80%E1%9F%84%E1%9E%93" title="កោន – Khmer" lang="km" hreflang="km" data-title="កោន" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="Khmer" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/C%C3%B2no" title="Còno – Piedmontese" lang="pms" hreflang="pms" data-title="Còno" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Sto%C5%BCek_(bry%C5%82a)" title="Stożek (bryła) – Polish" lang="pl" hreflang="pl" data-title="Stożek (bryła)" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Cone" title="Cone – Portuguese" lang="pt" hreflang="pt" data-title="Cone" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Con" title="Con – Romanian" lang="ro" hreflang="ro" data-title="Con" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Chuqu" title="Chuqu – Quechua" lang="qu" hreflang="qu" data-title="Chuqu" data-language-autonym="Runa Simi" data-language-local-name="Quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%83%D1%81" title="Конус – Russian" lang="ru" hreflang="ru" data-title="Конус" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Koni" title="Koni – Albanian" lang="sq" hreflang="sq" data-title="Koni" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Conu" title="Conu – Sicilian" lang="scn" hreflang="scn" data-title="Conu" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%9A%E0%B7%9A%E0%B6%AD%E0%B7%94%E0%B7%80" title="කේතුව – Sinhala" lang="si" hreflang="si" data-title="කේතුව" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Cone" title="Cone – Simple English" lang="en-simple" hreflang="en-simple" data-title="Cone" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Ku%C5%BEe%C4%BE" title="Kužeľ – Slovak" lang="sk" hreflang="sk" data-title="Kužeľ" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Sto%C5%BEec" title="Stožec – Slovenian" lang="sl" hreflang="sl" data-title="Stožec" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Toobin" title="Toobin – Somali" lang="so" hreflang="so" data-title="Toobin" data-language-autonym="Soomaaliga" data-language-local-name="Somali" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%82%D9%88%D9%88%DA%86%DB%95%DA%A9" title="قووچەک – Central Kurdish" lang="ckb" hreflang="ckb" data-title="قووچەک" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D1%83%D0%BF%D0%B0_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0)" title="Купа (геометрија) – Serbian" lang="sr" hreflang="sr" data-title="Купа (геометрија)" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Sto%C5%BEac" title="Stožac – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Stožac" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Congcot" title="Congcot – Sundanese" lang="su" hreflang="su" data-title="Congcot" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Kartio" title="Kartio – Finnish" lang="fi" hreflang="fi" data-title="Kartio" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Kon" title="Kon – Swedish" lang="sv" hreflang="sv" data-title="Kon" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Balisuso" title="Balisuso – Tagalog" lang="tl" hreflang="tl" data-title="Balisuso" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%95%E0%AF%82%E0%AE%AE%E0%AF%8D%E0%AE%AA%E0%AF%81" title="கூம்பு – Tamil" lang="ta" hreflang="ta" data-title="கூம்பு" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Akawsar_(tusnakt)" title="Akawsar (tusnakt) – Kabyle" lang="kab" hreflang="kab" data-title="Akawsar (tusnakt)" data-language-autonym="Taqbaylit" data-language-local-name="Kabyle" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%83%D1%81" title="Конус – Tatar" lang="tt" hreflang="tt" data-title="Конус" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%B6%E0%B0%82%E0%B0%95%E0%B1%81%E0%B0%B5%E0%B1%81" title="శంకువు – Telugu" lang="te" hreflang="te" data-title="శంకువు" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%97%E0%B8%A3%E0%B8%87%E0%B8%81%E0%B8%A3%E0%B8%A7%E0%B8%A2" title="ทรงกรวย – Thai" lang="th" hreflang="th" data-title="ทรงกรวย" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%83%D1%81" title="Конус – Tajik" lang="tg" hreflang="tg" data-title="Конус" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-chy mw-list-item"><a href="https://chy.wikipedia.org/wiki/Ts%C3%A9-%C3%A9%C5%A1k%C3%B4sa%27%C3%A9vetov%C3%A1to" title="Tsé-éškôsa'évetováto – Cheyenne" lang="chy" hreflang="chy" data-title="Tsé-éškôsa'évetováto" data-language-autonym="Tsetsêhestâhese" data-language-local-name="Cheyenne" class="interlanguage-link-target"><span>Tsetsêhestâhese</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Koni" title="Koni – Turkish" lang="tr" hreflang="tr" data-title="Koni" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tyv mw-list-item"><a href="https://tyv.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%83%D1%81" title="Конус – Tuvinian" lang="tyv" hreflang="tyv" data-title="Конус" data-language-autonym="Тыва дыл" data-language-local-name="Tuvinian" class="interlanguage-link-target"><span>Тыва дыл</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%83%D1%81" title="Конус – Ukrainian" lang="uk" hreflang="uk" data-title="Конус" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/M%E1%BA%B7t_n%C3%B3n" title="Mặt nón – Vietnamese" lang="vi" hreflang="vi" data-title="Mặt nón" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Cono_(heyometriya)" title="Cono (heyometriya) – Waray" lang="war" hreflang="war" data-title="Cono (heyometriya)" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%9C%86%E9%94%A5" title="圆锥 – Wu" lang="wuu" hreflang="wuu" data-title="圆锥" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A7%D7%90%D7%A0%D7%95%D7%A1" title="קאנוס – Yiddish" lang="yi" hreflang="yi" data-title="קאנוס" data-language-autonym="ייִדיש" data-language-local-name="Yiddish" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a 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class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Geometric shape</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For other uses, see <a href="/wiki/Cone_(disambiguation)" class="mw-disambig" title="Cone (disambiguation)">Cone (disambiguation)</a>.</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Not to be confused with <a href="/wiki/Conical_surface" title="Conical surface">Conical surface</a> or <a href="/wiki/Truncated_dome" class="mw-redirect" title="Truncated dome">Truncated dome</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox"><tbody><tr><th colspan="2" class="infobox-above" style="background:#e7dcc3">Cone</th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Cone_with_labeled_Radius,_Height,_Angle_and_Side.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3d/Cone_with_labeled_Radius%2C_Height%2C_Angle_and_Side.svg/220px-Cone_with_labeled_Radius%2C_Height%2C_Angle_and_Side.svg.png" decoding="async" width="220" height="124" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3d/Cone_with_labeled_Radius%2C_Height%2C_Angle_and_Side.svg/330px-Cone_with_labeled_Radius%2C_Height%2C_Angle_and_Side.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3d/Cone_with_labeled_Radius%2C_Height%2C_Angle_and_Side.svg/440px-Cone_with_labeled_Radius%2C_Height%2C_Angle_and_Side.svg.png 2x" data-file-width="576" data-file-height="324" /></a></span><div class="infobox-caption">A right circular cone with the radius of its base <i>r</i>, its height <i>h</i>, its slant height <i>c</i> and its angle <i>θ</i>.</div></td></tr><tr><th scope="row" class="infobox-label">Type</th><td class="infobox-data">Solid figure</td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Face_(geometry)" title="Face (geometry)">Faces</a></th><td class="infobox-data">1 circular face and 1 conic surface</td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Euler_characteristic" title="Euler characteristic">Euler char.</a></th><td class="infobox-data">2</td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/List_of_spherical_symmetry_groups" title="List of spherical symmetry groups">Symmetry group</a></th><td class="infobox-data"><a href="/wiki/Orthogonal_group" title="Orthogonal group"><span class="texhtml">O(2)</span></a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Surface_area" title="Surface area">Surface area</a></th><td class="infobox-data"><span class="texhtml"><a href="/wiki/Pi" title="Pi"><span class="texhtml mvar" style="font-style:italic;">π</span></a><i>r</i><sup>2</sup> + <a href="/wiki/Pi" title="Pi"><span class="texhtml mvar" style="font-style:italic;">π</span></a><i>rℓ</i></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Volume" title="Volume">Volume</a></th><td class="infobox-data"><span class="texhtml">(<a href="/wiki/Pi" title="Pi"><span class="texhtml mvar" style="font-style:italic;">π</span></a><i>r</i><sup>2</sup><i>h</i>)/3</span></td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Cone_3d.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Cone_3d.png/260px-Cone_3d.png" decoding="async" width="260" height="130" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Cone_3d.png/390px-Cone_3d.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Cone_3d.png/520px-Cone_3d.png 2x" data-file-width="913" data-file-height="458" /></a><figcaption>A right circular cone and an oblique circular cone</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:DoubleCone.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/DoubleCone.png/250px-DoubleCone.png" decoding="async" width="220" height="208" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/DoubleCone.png/330px-DoubleCone.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/72/DoubleCone.png/500px-DoubleCone.png 2x" data-file-width="1350" data-file-height="1274" /></a><figcaption>A double cone, not infinitely extended</figcaption></figure> <p>In <a href="/wiki/Geometry" title="Geometry">geometry</a>, a <b>cone</b> is a <a href="/wiki/Three-dimensional_figure" class="mw-redirect" title="Three-dimensional figure">three-dimensional figure</a> that tapers smoothly from a <a href="/wiki/Plane_(geometry)" class="mw-redirect" title="Plane (geometry)">flat</a> base (typically a <a href="/wiki/Circle" title="Circle">circle</a>) to a point not contained in the base, called the <i><a href="/wiki/Apex_(geometry)" title="Apex (geometry)">apex</a></i> or <i><a href="/wiki/Vertex_(geometry)" title="Vertex (geometry)">vertex</a></i>. </p><p>A cone is formed by a set of <a href="/wiki/Line_segment" title="Line segment">line segments</a>, <a href="/wiki/Ray_(geometry)" class="mw-redirect" title="Ray (geometry)">half-lines</a>, or <a href="/wiki/Line_(geometry)" title="Line (geometry)">lines</a> connecting a common point, the apex, to all of the points on a base. In the case of line segments, the cone does not extend beyond the base, while in the case of half-lines, it extends infinitely far. In the case of lines, the cone extends infinitely far in both directions from the apex, in which case it is sometimes called a <i>double cone</i><span class="anchor" id="Double"></span>. Each of the two halves of a double cone split at the apex is called a <i>nappe</i><span class="anchor" id="Nappe"></span>. </p><p>Depending on the author, the base may be restricted to a circle, any one-dimensional <a href="/wiki/Quadratic_form" title="Quadratic form">quadratic form</a> in the plane, any closed <a href="/wiki/One-dimensional_space" title="One-dimensional space">one-dimensional figure</a>, or any of the above plus all the enclosed points. If the enclosed points are included in the base, the cone is a <a href="/wiki/Solid_geometry" title="Solid geometry">solid object</a>; otherwise it is an <a href="/wiki/Open_surface" class="mw-redirect" title="Open surface">open surface</a>, a <a href="/wiki/Two-dimensional" class="mw-redirect" title="Two-dimensional">two-dimensional</a> object in three-dimensional space. In the case of a solid object, the boundary formed by these lines or partial lines is called the <i>lateral surface</i>; if the lateral surface is <a href="/wiki/Unbounded_set" class="mw-redirect" title="Unbounded set">unbounded</a>, it is a <i><a href="/wiki/Conical_surface" title="Conical surface">conical surface</a></i>. </p><p>The <a href="/wiki/Rotational_symmetry" title="Rotational symmetry">axis</a> of a cone is the straight line passing through the apex about which the cone has a <a href="/wiki/Circular_symmetry" title="Circular symmetry">circular symmetry</a>. <span class="anchor" id="Right_circular"></span>In common usage in elementary geometry, cones are assumed to be <i>right circular</i>, i.e., with a circle base <a href="/wiki/Perpendicular" title="Perpendicular">perpendicular</a> to the axis.<sup id="cite_ref-:1_1-0" class="reference"><a href="#cite_note-:1-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> If the cone is right circular the intersection of a plane with the lateral surface is a <a href="/wiki/Conic_section" title="Conic section">conic section</a>. In general, however, the base may be any shape<sup id="cite_ref-grunbaum_2-0" class="reference"><a href="#cite_note-grunbaum-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> and the apex may lie anywhere (though it is usually assumed that the base is bounded and therefore has finite <a href="/wiki/Area_(geometry)" class="mw-redirect" title="Area (geometry)">area</a>, and that the apex lies outside the plane of the base). Contrasted with right cones are <i>oblique cones</i>, in which the axis passes through the centre of the base non-perpendicularly.<sup id="cite_ref-MathWorld_3-0" class="reference"><a href="#cite_note-MathWorld-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>Depending on context, <i>cone</i> may refer more narrowly to either a <a href="/wiki/Convex_cone" title="Convex cone">convex cone</a> or <a href="/wiki/Projective_cone" title="Projective cone">projective cone</a>. Cones can be generalized to <a href="/wiki/Dimension#Additional_dimensions" title="Dimension">higher dimensions</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Further_terminology">Further terminology <span class="anchor" id="Terminology"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cone&action=edit&section=1" title="Edit section: Further terminology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The perimeter of the base of a cone is called the <i>directrix</i>, and each of the line segments between the directrix and apex is a <i>generatrix</i> or <i>generating line</i> of the lateral surface. (For the connection between this sense of the term <i>directrix</i> and the <a href="/wiki/Directrix_(conic_section)" class="mw-redirect" title="Directrix (conic section)">directrix</a> of a conic section, see <a href="/wiki/Dandelin_spheres" title="Dandelin spheres">Dandelin spheres</a>.) </p><p>The <i>base radius</i> of a circular cone is the <a href="/wiki/Radius" title="Radius">radius</a> of its base; often this is simply called the radius of the cone. <span class="anchor" id="Aperture"></span>The <i>aperture</i> of a right circular cone is the maximum angle between two generatrix lines; if the generatrix makes an angle <i>θ</i> to the axis, the aperture is 2<i>θ</i>. In <a href="/wiki/Optics" title="Optics">optics</a>, the angle <i>θ</i> is called the <span class="anchor" id="half-angle"></span><i>half-angle</i> of the cone, to distinguish it from the aperture. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Acta_Eruditorum_-_I_geometria,_1734_%E2%80%93_BEIC_13446956.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/68/Acta_Eruditorum_-_I_geometria%2C_1734_%E2%80%93_BEIC_13446956.jpg/250px-Acta_Eruditorum_-_I_geometria%2C_1734_%E2%80%93_BEIC_13446956.jpg" decoding="async" width="220" height="270" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/68/Acta_Eruditorum_-_I_geometria%2C_1734_%E2%80%93_BEIC_13446956.jpg/330px-Acta_Eruditorum_-_I_geometria%2C_1734_%E2%80%93_BEIC_13446956.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/68/Acta_Eruditorum_-_I_geometria%2C_1734_%E2%80%93_BEIC_13446956.jpg/500px-Acta_Eruditorum_-_I_geometria%2C_1734_%E2%80%93_BEIC_13446956.jpg 2x" data-file-width="1076" data-file-height="1322" /></a><figcaption>Illustration from <i>Problemata mathematica...</i> published in <a href="/wiki/Acta_Eruditorum" title="Acta Eruditorum">Acta Eruditorum</a>, 1734</figcaption></figure> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Cut_cone_unparallel.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/14/Cut_cone_unparallel.JPG" decoding="async" width="220" height="216" class="mw-file-element" data-file-width="220" data-file-height="216" /></a><figcaption>A cone truncated by an inclined plane</figcaption></figure> <p>A cone with a region including its apex cut off by a plane is called a <i>truncated cone</i>; if the <a href="/wiki/Truncation_(geometry)" title="Truncation (geometry)">truncation</a> plane is parallel to the cone's base, it is called a <i><a href="/wiki/Frustum" title="Frustum">frustum</a></i>.<sup id="cite_ref-:1_1-1" class="reference"><a href="#cite_note-:1-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> An <i>elliptical cone</i> is a cone with an <a href="/wiki/Ellipse" title="Ellipse">elliptical</a> base.<sup id="cite_ref-:1_1-2" class="reference"><a href="#cite_note-:1-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> A <i>generalized cone</i> is the surface created by the set of lines passing through a vertex and every point on a boundary (see <a href="/wiki/Visual_hull" title="Visual hull">Visual hull</a>). </p> <div class="mw-heading mw-heading2"><h2 id="Measurements_and_equations">Measurements and equations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cone&action=edit&section=2" title="Edit section: Measurements and equations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Volume">Volume</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cone&action=edit&section=3" title="Edit section: Volume"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Visual_proof_cone_volume.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Visual_proof_cone_volume.svg/250px-Visual_proof_cone_volume.svg.png" decoding="async" width="220" height="293" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Visual_proof_cone_volume.svg/330px-Visual_proof_cone_volume.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Visual_proof_cone_volume.svg/500px-Visual_proof_cone_volume.svg.png 2x" data-file-width="512" data-file-height="683" /></a><figcaption><a href="/wiki/Proof_without_words" title="Proof without words">Proof without words</a> that the volume of a cone is a third of a cylinder of equal diameter and height <table> <tbody><tr> <td valign="top"><span class="nowrap">1.</span></td> <td>A cone and a cylinder have <span class="nowrap">radius <i>r</i></span> and <span class="nowrap">height <i>h</i>.</span> </td></tr> <tr> <td valign="top">2.</td> <td>The volume ratio is maintained when the height is scaled to <span class="nowrap"><i>h' </i>= <i>r</i> √<span class="texhtml mvar" style="font-style:italic;">π</span>.</span> </td></tr> <tr> <td valign="top">3.</td> <td>Decompose it into thin slices. </td></tr> <tr> <td valign="top">4.</td> <td>Using Cavalieri's principle, reshape each slice into a square of the same area. </td></tr> <tr> <td valign="top">5.</td> <td>The pyramid is replicated twice. </td></tr> <tr> <td valign="top">6.</td> <td>Combining them into a cube shows that the volume ratio is 1:3. </td></tr></tbody></table></figcaption></figure> <p>The <a href="/wiki/Volume" title="Volume">volume</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}" /></span> of any conic solid is one third of the product of the area of the base <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{B}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{B}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40c23902854ca17ed340b014fda4b3e6adc02b46" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.223ex; height:2.509ex;" alt="{\displaystyle A_{B}}" /></span> and the height <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b26be3e694314bc90c3215047e4a2010c6ee184a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.339ex; height:2.176ex;" alt="{\displaystyle h}" /></span><sup id="cite_ref-:0_4-0" class="reference"><a href="#cite_note-:0-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V={\frac {1}{3}}A_{B}h.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> </mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>h</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V={\frac {1}{3}}A_{B}h.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e37289a6c713019fa691146d8af5a49a81eadf16" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.093ex; height:5.176ex;" alt="{\displaystyle V={\frac {1}{3}}A_{B}h.}" /></span> </p><p>In modern mathematics, this formula can easily be computed using calculus — it is, up to scaling, the integral </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int x^{2}\,dx={\tfrac {1}{3}}x^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> </mstyle> </mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int x^{2}\,dx={\tfrac {1}{3}}x^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2220beda63bd2cb350b048d4651c94c6d9de18d1" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:15.038ex; height:5.676ex;" alt="{\displaystyle \int x^{2}\,dx={\tfrac {1}{3}}x^{3}}" /></span> </p><p>Without using calculus, the formula can be proven by comparing the cone to a pyramid and applying <a href="/wiki/Cavalieri%27s_principle" title="Cavalieri's principle">Cavalieri's principle</a> – specifically, comparing the cone to a (vertically scaled) right square pyramid, which forms one third of a cube. This formula cannot be proven without using such infinitesimal arguments – unlike the 2-dimensional formulae for polyhedral area, though similar to the area of the circle – and hence admitted less rigorous proofs before the advent of calculus, with the ancient Greeks using the <a href="/wiki/Method_of_exhaustion" title="Method of exhaustion">method of exhaustion</a>. This is essentially the content of <a href="/wiki/Hilbert%27s_third_problem" title="Hilbert's third problem">Hilbert's third problem</a> – more precisely, not all polyhedral pyramids are <i>scissors congruent</i> (can be cut apart into finite pieces and rearranged into the other), and thus volume cannot be computed purely by using a decomposition argument.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Center_of_mass">Center of mass</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cone&action=edit&section=4" title="Edit section: Center of mass"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Center_of_mass" title="Center of mass">center of mass</a> of a conic solid of uniform density lies one-quarter of the way from the center of the base to the vertex, on the straight line joining the two. </p> <div class="mw-heading mw-heading3"><h3 id="Right_circular_cone">Right circular cone</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cone&action=edit&section=5" title="Edit section: Right circular cone"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Volume_2">Volume</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cone&action=edit&section=6" title="Edit section: Volume"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For a circular cone with radius <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}" /></span> and height <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b26be3e694314bc90c3215047e4a2010c6ee184a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.339ex; height:2.176ex;" alt="{\displaystyle h}" /></span>, the base is a circle of area <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi r^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi r^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd37db3982ad4e1157dcf8ddbfb280e7bae3b192" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.435ex; height:2.676ex;" alt="{\displaystyle \pi r^{2}}" /></span> thus the formula for volume is:<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V={\frac {1}{3}}\pi r^{2}h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> </mrow> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V={\frac {1}{3}}\pi r^{2}h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8148cf955aa0660882254207e18ef9bf92463d8c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:11.658ex; height:5.176ex;" alt="{\displaystyle V={\frac {1}{3}}\pi r^{2}h}" /></span> </p> <div class="mw-heading mw-heading4"><h4 id="Slant_height">Slant height</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cone&action=edit&section=7" title="Edit section: Slant height"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Slant_height" class="mw-redirect" title="Slant height">slant height</a> of a right circular cone is the distance from any point on the <a href="/wiki/Circle" title="Circle">circle</a> of its base to the apex via a line segment along the surface of the cone. It is given by <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {r^{2}+h^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {r^{2}+h^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97c4fed1ecfaead926d51fd4b71343adc10e1fc8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.66ex; height:3.509ex;" alt="{\displaystyle {\sqrt {r^{2}+h^{2}}}}" /></span>, where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}" /></span> is the <a href="/wiki/Radius" title="Radius">radius</a> of the base and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b26be3e694314bc90c3215047e4a2010c6ee184a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.339ex; height:2.176ex;" alt="{\displaystyle h}" /></span> is the height. This can be proved by the <a href="/wiki/Pythagorean_theorem" title="Pythagorean theorem">Pythagorean theorem</a>. </p> <div class="mw-heading mw-heading4"><h4 id="Surface_area">Surface area</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cone&action=edit&section=8" title="Edit section: Surface area"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Lateral_surface" title="Lateral surface">lateral surface</a> area of a right circular cone is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle LSA=\pi r\ell }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mi>S</mi> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mi>r</mi> <mi>ℓ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle LSA=\pi r\ell }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5eff8a627478fd1c2974ee9d626872b8ef7b62c0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.274ex; height:2.176ex;" alt="{\displaystyle LSA=\pi r\ell }" /></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}" /></span> is the radius of the circle at the bottom of the cone and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ell }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ℓ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ell }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f066e981e530bacc07efc6a10fa82deee985929e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.97ex; height:2.176ex;" alt="{\displaystyle \ell }" /></span> is the slant height of the cone.<sup id="cite_ref-:0_4-1" class="reference"><a href="#cite_note-:0-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> The surface area of the bottom circle of a cone is the same as for any circle, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi r^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi r^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd37db3982ad4e1157dcf8ddbfb280e7bae3b192" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.435ex; height:2.676ex;" alt="{\displaystyle \pi r^{2}}" /></span>. Thus, the total surface area of a right circular cone can be expressed as each of the following: </p> <ul><li>Radius and height</li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi r^{2}+\pi r{\sqrt {r^{2}+h^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>π</mi> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi r^{2}+\pi r{\sqrt {r^{2}+h^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f2443cfc0f3264499b90d9285a29be7099f77e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.316ex; height:3.509ex;" alt="{\displaystyle \pi r^{2}+\pi r{\sqrt {r^{2}+h^{2}}}}" /></span></dd></dl></dd> <dd>(the area of the base plus the area of the lateral surface; the term <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {r^{2}+h^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {r^{2}+h^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97c4fed1ecfaead926d51fd4b71343adc10e1fc8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.66ex; height:3.509ex;" alt="{\displaystyle {\sqrt {r^{2}+h^{2}}}}" /></span> is the slant height)</dd></dl> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi r\left(r+{\sqrt {r^{2}+h^{2}}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <mi>r</mi> <mrow> <mo>(</mo> <mrow> <mi>r</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi r\left(r+{\sqrt {r^{2}+h^{2}}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41aca8f13a1e2996128c0ae640d7261682edf793" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:19.093ex; height:4.843ex;" alt="{\displaystyle \pi r\left(r+{\sqrt {r^{2}+h^{2}}}\right)}" /></span></dd></dl></dd> <dd>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}" /></span> is the radius and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b26be3e694314bc90c3215047e4a2010c6ee184a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.339ex; height:2.176ex;" alt="{\displaystyle h}" /></span> is the height.</dd></dl> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Cone_surface_area.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/Cone_surface_area.svg/250px-Cone_surface_area.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/Cone_surface_area.svg/330px-Cone_surface_area.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/56/Cone_surface_area.svg/500px-Cone_surface_area.svg.png 2x" data-file-width="512" data-file-height="512" /></a><figcaption>Total surface area of a right circular cone, given radius 𝑟 and slant height ℓ</figcaption></figure> <ul><li>Radius and slant height</li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi r^{2}+\pi r\ell }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>π</mi> <mi>r</mi> <mi>ℓ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi r^{2}+\pi r\ell }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/124de3a6586be87ee7b7537ff042f54c223b62f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.626ex; height:2.843ex;" alt="{\displaystyle \pi r^{2}+\pi r\ell }" /></span></dd></dl></dd></dl> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi r(r+\ell )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <mi>r</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo>+</mo> <mi>ℓ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi r(r+\ell )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac06f69d120edb7fe92504d84e4f93fb87d02439" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.049ex; height:2.843ex;" alt="{\displaystyle \pi r(r+\ell )}" /></span></dd></dl></dd> <dd>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}" /></span> is the radius and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ell }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ℓ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ell }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f066e981e530bacc07efc6a10fa82deee985929e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.97ex; height:2.176ex;" alt="{\displaystyle \ell }" /></span> is the slant height.</dd></dl> <ul><li>Circumference and slant height</li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {c^{2}}{4\pi }}+{\frac {c\ell }{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>4</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>c</mi> <mi>ℓ</mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {c^{2}}{4\pi }}+{\frac {c\ell }{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e61bad7388aff8e5fc0d5131e1b13d8a36dac6c6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:8.984ex; height:5.676ex;" alt="{\displaystyle {\frac {c^{2}}{4\pi }}+{\frac {c\ell }{2}}}" /></span></dd></dl></dd></dl> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {c}{2}}\right)\left({\frac {c}{2\pi }}+\ell \right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>c</mi> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>c</mi> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>ℓ</mi> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {c}{2}}\right)\left({\frac {c}{2\pi }}+\ell \right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/828e2bc50a5dea7a40f6a756fab80fbdb15fa4b4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:15.077ex; height:4.843ex;" alt="{\displaystyle \left({\frac {c}{2}}\right)\left({\frac {c}{2\pi }}+\ell \right)}" /></span></dd></dl></dd> <dd>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}" /></span> is the circumference and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ell }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ℓ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ell }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f066e981e530bacc07efc6a10fa82deee985929e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.97ex; height:2.176ex;" alt="{\displaystyle \ell }" /></span> is the slant height.</dd></dl> <ul><li>Apex angle and height</li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi h^{2}\tan {\frac {\theta }{2}}\left(\tan {\frac {\theta }{2}}+\sec {\frac {\theta }{2}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>tan</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>θ</mi> <mn>2</mn> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mi>tan</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>θ</mi> <mn>2</mn> </mfrac> </mrow> <mo>+</mo> <mi>sec</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>θ</mi> <mn>2</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi h^{2}\tan {\frac {\theta }{2}}\left(\tan {\frac {\theta }{2}}+\sec {\frac {\theta }{2}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b37430e7d4ed26d13f564348ae8d0ba54a5a9d06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:27.618ex; height:6.176ex;" alt="{\displaystyle \pi h^{2}\tan {\frac {\theta }{2}}\left(\tan {\frac {\theta }{2}}+\sec {\frac {\theta }{2}}\right)}" /></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -{\frac {\pi h^{2}\sin {\frac {\theta }{2}}}{\sin {\frac {\theta }{2}}-1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>π</mi> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>sin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>θ</mi> <mn>2</mn> </mfrac> </mrow> </mrow> <mrow> <mi>sin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>θ</mi> <mn>2</mn> </mfrac> </mrow> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -{\frac {\pi h^{2}\sin {\frac {\theta }{2}}}{\sin {\frac {\theta }{2}}-1}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb3247e3666d3c2921a25ca65f9833203b6c2249" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.505ex; width:11.657ex; height:8.176ex;" alt="{\displaystyle -{\frac {\pi h^{2}\sin {\frac {\theta }{2}}}{\sin {\frac {\theta }{2}}-1}}}" /></span></dd></dl></dd> <dd>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }" /></span> is the apex angle and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b26be3e694314bc90c3215047e4a2010c6ee184a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.339ex; height:2.176ex;" alt="{\displaystyle h}" /></span> is the height.</dd></dl> <div class="mw-heading mw-heading4"><h4 id="Circular_sector">Circular sector</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cone&action=edit&section=9" title="Edit section: Circular sector"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Circular_sector" title="Circular sector">circular sector</a> is obtained by unfolding the surface of one nappe of the cone: </p> <ul><li>radius <i>R</i></li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R={\sqrt {r^{2}+h^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R={\sqrt {r^{2}+h^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d62b48d34cc2b88a229b3bcf8e8d7103fe355fd5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.523ex; height:3.509ex;" alt="{\displaystyle R={\sqrt {r^{2}+h^{2}}}}" /></span></dd></dl></dd></dl> <ul><li>arc length <i>L</i></li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L=c=2\pi r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>=</mo> <mi>c</mi> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L=c=2\pi r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa785c6bb2c87e86d4d393dd98b968db6808615a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:12.33ex; height:2.176ex;" alt="{\displaystyle L=c=2\pi r}" /></span></dd></dl></dd></dl> <ul><li>central angle <i>φ</i> in radians</li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi ={\frac {L}{R}}={\frac {2\pi r}{\sqrt {r^{2}+h^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>L</mi> <mi>R</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> <mi>r</mi> </mrow> <msqrt> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi ={\frac {L}{R}}={\frac {2\pi r}{\sqrt {r^{2}+h^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae78b15489abf7d3a9ec9443887aba34e7c18f40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:20.814ex; height:6.509ex;" alt="{\displaystyle \varphi ={\frac {L}{R}}={\frac {2\pi r}{\sqrt {r^{2}+h^{2}}}}}" /></span></dd></dl></dd></dl> <div class="mw-heading mw-heading4"><h4 id="Equation_form">Equation form</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cone&action=edit&section=10" title="Edit section: Equation form"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The surface of a cone can be parameterized as </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(\theta ,h)=(h\cos \theta ,h\sin \theta ,h),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>θ</mi> <mo>,</mo> <mi>h</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mi>h</mi> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> <mo>,</mo> <mi>h</mi> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> <mo>,</mo> <mi>h</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(\theta ,h)=(h\cos \theta ,h\sin \theta ,h),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/16385b6133035c3d87937f04e22c141cd5c15e1f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.887ex; height:2.843ex;" alt="{\displaystyle f(\theta ,h)=(h\cos \theta ,h\sin \theta ,h),}" /></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta \in [0,2\pi )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mn>2</mn> <mi>π</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta \in [0,2\pi )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd6198e2678333f87b41d13a47e94c7b2567d8ea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.173ex; height:2.843ex;" alt="{\displaystyle \theta \in [0,2\pi )}" /></span> is the angle "around" the cone, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h\in \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h\in \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/abf67cfa06f841b9b56ef83e0325f93da1257134" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.858ex; height:2.176ex;" alt="{\displaystyle h\in \mathbb {R} }" /></span> is the "height" along the cone. </p><p>A right solid circular cone with height <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b26be3e694314bc90c3215047e4a2010c6ee184a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.339ex; height:2.176ex;" alt="{\displaystyle h}" /></span> and aperture <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2\theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/493f1772ffdb7096362a9de2d587b65a79f4b6f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.253ex; height:2.176ex;" alt="{\displaystyle 2\theta }" /></span>, whose axis is the <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf368e72c009decd9b6686ee84a375632e11de98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.088ex; height:1.676ex;" alt="{\displaystyle z}" /></span> coordinate axis and whose apex is the origin, is described parametrically as </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(s,t,u)=\left(u\tan s\cos t,u\tan s\sin t,u\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mi>s</mi> <mo>,</mo> <mi>t</mi> <mo>,</mo> <mi>u</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mi>u</mi> <mi>tan</mi> <mo>⁡</mo> <mi>s</mi> <mi>cos</mi> <mo>⁡</mo> <mi>t</mi> <mo>,</mo> <mi>u</mi> <mi>tan</mi> <mo>⁡</mo> <mi>s</mi> <mi>sin</mi> <mo>⁡</mo> <mi>t</mi> <mo>,</mo> <mi>u</mi> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(s,t,u)=\left(u\tan s\cos t,u\tan s\sin t,u\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e99d6f7d16583141523a83b485905fb5dc5f0002" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:39.485ex; height:2.843ex;" alt="{\displaystyle F(s,t,u)=\left(u\tan s\cos t,u\tan s\sin t,u\right)}" /></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s,t,u}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> <mo>,</mo> <mi>t</mi> <mo>,</mo> <mi>u</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s,t,u}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be86046a144c712651e85eb2168015bf76ced0d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.328ex; height:2.343ex;" alt="{\displaystyle s,t,u}" /></span> range over <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [0,\theta )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mi>θ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [0,\theta )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c820e0ca749c621ecc3633cdf2d76470db4ddbb9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.838ex; height:2.843ex;" alt="{\displaystyle [0,\theta )}" /></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [0,2\pi )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mn>2</mn> <mi>π</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [0,2\pi )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ec72cfde732f42822df3cbbe175b7465887eb80" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.242ex; height:2.843ex;" alt="{\displaystyle [0,2\pi )}" /></span>, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [0,h]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mi>h</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [0,h]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dbede90a8f7ff59267c875f09e715c896ce7a51a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.829ex; height:2.843ex;" alt="{\displaystyle [0,h]}" /></span>, respectively. </p><p>In <a href="/wiki/Implicit_function" title="Implicit function">implicit</a> form, the same solid is defined by the inequalities </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \{F(x,y,z)\leq 0,z\geq 0,z\leq h\},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>≤</mo> <mn>0</mn> <mo>,</mo> <mi>z</mi> <mo>≥</mo> <mn>0</mn> <mo>,</mo> <mi>z</mi> <mo>≤</mo> <mi>h</mi> <mo fence="false" stretchy="false">}</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{F(x,y,z)\leq 0,z\geq 0,z\leq h\},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da630de2ecec4d02dbe4b0b1a407fde2f5adca03" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:29.366ex; height:2.843ex;" alt="{\displaystyle \{F(x,y,z)\leq 0,z\geq 0,z\leq h\},}" /></span></dd></dl> <p>where </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(x,y,z)=(x^{2}+y^{2})(\cos \theta )^{2}-z^{2}(\sin \theta )^{2}.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>.</mo> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(x,y,z)=(x^{2}+y^{2})(\cos \theta )^{2}-z^{2}(\sin \theta )^{2}.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6042fb68e79d600676d2af3f0ab09294e9d03b18" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:42.206ex; height:3.176ex;" alt="{\displaystyle F(x,y,z)=(x^{2}+y^{2})(\cos \theta )^{2}-z^{2}(\sin \theta )^{2}.\,}" /></span></dd></dl> <p>More generally, a right circular cone with vertex at the origin, axis parallel to the vector <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.216ex; height:2.176ex;" alt="{\displaystyle d}" /></span>, and aperture <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2\theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/493f1772ffdb7096362a9de2d587b65a79f4b6f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.253ex; height:2.176ex;" alt="{\displaystyle 2\theta }" /></span>, is given by the implicit <a href="/wiki/Vector_calculus" title="Vector calculus">vector</a> equation <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(u)=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mi>u</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(u)=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e2b680a7dc8169d25fba56114a9b7c68edbb2d48" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.141ex; height:2.843ex;" alt="{\displaystyle F(u)=0}" /></span> where </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(u)=(u\cdot d)^{2}-(d\cdot d)(u\cdot u)(\cos \theta )^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mi>u</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mi>u</mi> <mo>⋅</mo> <mi>d</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mo stretchy="false">(</mo> <mi>d</mi> <mo>⋅</mo> <mi>d</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>u</mi> <mo>⋅</mo> <mi>u</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(u)=(u\cdot d)^{2}-(d\cdot d)(u\cdot u)(\cos \theta )^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63a042d8213ca188da44d4c8e5781e8cfe084744" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:37.427ex; height:3.176ex;" alt="{\displaystyle F(u)=(u\cdot d)^{2}-(d\cdot d)(u\cdot u)(\cos \theta )^{2}}" /></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(u)=u\cdot d-|d||u|\cos \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mi>u</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>u</mi> <mo>⋅</mo> <mi>d</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(u)=u\cdot d-|d||u|\cos \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/746c1410cc1b336e48898d3bb1c968c6ca068e35" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.152ex; height:2.843ex;" alt="{\displaystyle F(u)=u\cdot d-|d||u|\cos \theta }" /></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u=(x,y,z)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> <mo>=</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u=(x,y,z)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c859cf3150346d60ba03189cefdd0290d4c17861" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.879ex; height:2.843ex;" alt="{\displaystyle u=(x,y,z)}" /></span>, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u\cdot d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> <mo>⋅</mo> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u\cdot d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e2ac43224e648965087c181c6edde954ab52a524" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.225ex; height:2.176ex;" alt="{\displaystyle u\cdot d}" /></span> denotes the <a href="/wiki/Dot_product" title="Dot product">dot product</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Elliptic_cone">Elliptic cone</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cone&action=edit&section=11" title="Edit section: Elliptic cone"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Elliptical_Cone_Quadric.Png" class="mw-file-description"><img alt="elliptical cone quadric surface" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Elliptical_Cone_Quadric.Png/220px-Elliptical_Cone_Quadric.Png" decoding="async" width="220" height="243" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Elliptical_Cone_Quadric.Png/330px-Elliptical_Cone_Quadric.Png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Elliptical_Cone_Quadric.Png/440px-Elliptical_Cone_Quadric.Png 2x" data-file-width="750" data-file-height="829" /></a><figcaption>An elliptical cone quadric surface</figcaption></figure> <p>In the <a href="/wiki/Cartesian_coordinate_system" title="Cartesian coordinate system">Cartesian coordinate system</a>, an <i>elliptic cone</i> is the <a href="/wiki/Locus_(mathematics)" title="Locus (mathematics)">locus</a> of an equation of the form<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {x^{2}}{a^{2}}}+{\frac {y^{2}}{b^{2}}}=z^{2}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {x^{2}}{a^{2}}}+{\frac {y^{2}}{b^{2}}}=z^{2}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/14b603fddcb01a3ab642d0d432207e529ee30e2a" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:15.001ex; height:6.009ex;" alt="{\displaystyle {\frac {x^{2}}{a^{2}}}+{\frac {y^{2}}{b^{2}}}=z^{2}.}" /></span> </p><p>It is an <a href="/wiki/Affine_map" class="mw-redirect" title="Affine map">affine image</a> of the right-circular <i>unit cone</i> with equation <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{2}+y^{2}=z^{2}\ .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mtext> </mtext> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}+y^{2}=z^{2}\ .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48ee56a974d71a87af039a9f89060fa04c288526" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.91ex; height:3.009ex;" alt="{\displaystyle x^{2}+y^{2}=z^{2}\ .}" /></span> From the fact, that the affine image of a <a href="/wiki/Conic_section" title="Conic section">conic section</a> is a conic section of the same type (ellipse, parabola,...), one gets: </p> <ul><li>Any <i>plane section</i> of an elliptic cone is a conic section.</li></ul> <p>Obviously, any right circular cone contains circles. This is also true, but less obvious, in the general case (see <a href="/wiki/Circular_section" title="Circular section">circular section</a>). </p><p>The intersection of an elliptic cone with a concentric sphere is a <a href="/wiki/Spherical_conic" title="Spherical conic">spherical conic</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Projective_geometry">Projective geometry</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cone&action=edit&section=12" title="Edit section: Projective geometry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Australia_Square_building_in_George_Street_Sydney.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Australia_Square_building_in_George_Street_Sydney.jpg/130px-Australia_Square_building_in_George_Street_Sydney.jpg" decoding="async" width="130" height="264" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Australia_Square_building_in_George_Street_Sydney.jpg/195px-Australia_Square_building_in_George_Street_Sydney.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Australia_Square_building_in_George_Street_Sydney.jpg/260px-Australia_Square_building_in_George_Street_Sydney.jpg 2x" data-file-width="1376" data-file-height="2791" /></a><figcaption>In <a href="/wiki/Projective_geometry" title="Projective geometry">projective geometry</a>, a <a href="/wiki/Cylinder_(geometry)" class="mw-redirect" title="Cylinder (geometry)">cylinder</a> is simply a cone whose apex is at infinity, which corresponds visually to a cylinder in perspective appearing to be a cone towards the sky.</figcaption></figure> <p>In <a href="/wiki/Projective_geometry" title="Projective geometry">projective geometry</a>, a <a href="/wiki/Cylinder_(geometry)" class="mw-redirect" title="Cylinder (geometry)">cylinder</a> is simply a cone whose apex is at infinity.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Intuitively, if one keeps the base fixed and takes the limit as the apex goes to infinity, one obtains a cylinder, the angle of the side increasing as <a href="/wiki/Arctan" class="mw-redirect" title="Arctan">arctan</a>, in the limit forming a <a href="/wiki/Right_angle" title="Right angle">right angle</a>. This is useful in the definition of <a href="/wiki/Degenerate_conic" title="Degenerate conic">degenerate conics</a>, which require considering the <a href="/w/index.php?title=Cylindrical_conic&action=edit&redlink=1" class="new" title="Cylindrical conic (page does not exist)">cylindrical conics</a>. </p><p>According to <a href="/wiki/G._B._Halsted" title="G. B. Halsted">G. B. Halsted</a>, a cone is generated similarly to a <a href="/wiki/Steiner_conic" title="Steiner conic">Steiner conic</a> only with a projectivity and <a href="/wiki/Pencil_(mathematics)" class="mw-redirect" title="Pencil (mathematics)">axial pencils</a> (not in perspective) rather than the projective ranges used for the Steiner conic: </p><p>"If two copunctual non-costraight axial pencils are projective but not perspective, the meets of correlated planes form a 'conic surface of the second order', or 'cone'."<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Generalizations">Generalizations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cone&action=edit&section=13" title="Edit section: Generalizations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Hypercone" title="Hypercone">Hypercone</a></div> <p>The definition of a cone may be extended to higher dimensions; see <a href="/wiki/Convex_cone" title="Convex cone">convex cone</a>. In this case, one says that a <a href="/wiki/Convex_set" title="Convex set">convex set</a> <i>C</i> in the <a href="/wiki/Real_number" title="Real number">real</a> <a href="/wiki/Vector_space" title="Vector space">vector space</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} ^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} ^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.897ex; height:2.343ex;" alt="{\displaystyle \mathbb {R} ^{n}}" /></span> is a cone (with apex at the origin) if for every vector <i>x</i> in <i>C</i> and every nonnegative real number <i>a</i>, the vector <i>ax</i> is in <i>C</i>.<sup id="cite_ref-grunbaum_2-1" class="reference"><a href="#cite_note-grunbaum-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> In this context, the analogues of circular cones are not usually special; in fact one is often interested in <a href="/wiki/Convex_cone#Polyhedral_and_finitely_generated_cones" title="Convex cone">polyhedral cones</a>. </p><p>An even more general concept is the <a href="/wiki/Topological_cone" class="mw-redirect" title="Topological cone">topological cone</a>, which is defined in arbitrary topological spaces. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cone&action=edit&section=14" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Bicone" title="Bicone">Bicone</a></li> <li><a href="/wiki/Cone_(linear_algebra)" class="mw-redirect" title="Cone (linear algebra)">Cone (linear algebra)</a></li> <li><a href="/wiki/Cylinder_(geometry)" class="mw-redirect" title="Cylinder (geometry)">Cylinder (geometry)</a></li> <li><a href="/wiki/Democritus#Mathematics" title="Democritus">Democritus</a></li> <li><a href="/wiki/Generalized_conic" title="Generalized conic">Generalized conic</a></li> <li><a href="/wiki/Hyperboloid" title="Hyperboloid">Hyperboloid</a></li> <li><a href="/wiki/List_of_shapes" class="mw-redirect" title="List of shapes">List of shapes</a></li> <li><a href="/wiki/Pyrometric_cone" title="Pyrometric cone">Pyrometric cone</a></li> <li><a href="/wiki/Quadric" title="Quadric">Quadric</a></li> <li><a href="/wiki/Rotation_of_axes" class="mw-redirect" title="Rotation of axes">Rotation of axes</a></li> <li><a href="/wiki/Ruled_surface" title="Ruled surface">Ruled surface</a></li> <li><a href="/wiki/Translation_of_axes" title="Translation of axes">Translation of axes</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cone&action=edit&section=15" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-:1-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:1_1-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFJamesJames1992" class="citation book cs1"><a href="/wiki/Robert_C._James" title="Robert C. James">James, R. C.</a>; James, Glenn (1992-07-31). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=UyIfgBIwLMQC"><i>The Mathematics Dictionary</i></a>. Springer Science & Business Media. pp. <span class="nowrap">74–</span>75. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780412990410" title="Special:BookSources/9780412990410"><bdi>9780412990410</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Mathematics+Dictionary&rft.pages=%3Cspan+class%3D%22nowrap%22%3E74-%3C%2Fspan%3E75&rft.pub=Springer+Science+%26+Business+Media&rft.date=1992-07-31&rft.isbn=9780412990410&rft.aulast=James&rft.aufirst=R.+C.&rft.au=James%2C+Glenn&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DUyIfgBIwLMQC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACone" class="Z3988"></span></span> </li> <li id="cite_note-grunbaum-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-grunbaum_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-grunbaum_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Grünbaum, <i><a href="/wiki/Convex_Polytopes" title="Convex Polytopes">Convex Polytopes</a></i>, second edition, p. 23.</span> </li> <li id="cite_note-MathWorld-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-MathWorld_3-0">^</a></b></span> <span class="reference-text"><span class="citation mathworld" id="Reference-Mathworld-Cone"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFWeisstein" class="citation web cs1"><a href="/wiki/Eric_W._Weisstein" title="Eric W. Weisstein">Weisstein, Eric W.</a> <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/Cone.html">"Cone"</a>. <i><a href="/wiki/MathWorld" title="MathWorld">MathWorld</a></i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=MathWorld&rft.atitle=Cone&rft.au=Weisstein%2C+Eric+W.&rft_id=https%3A%2F%2Fmathworld.wolfram.com%2FCone.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACone" class="Z3988"></span></span></span> </li> <li id="cite_note-:0-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_4-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFAlexanderKoeberlein2014" class="citation book cs1">Alexander, Daniel C.; Koeberlein, Geralyn M. (2014-01-01). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=EN_KAgAAQBAJ"><i>Elementary Geometry for College Students</i></a>. Cengage. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781285965901" title="Special:BookSources/9781285965901"><bdi>9781285965901</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Elementary+Geometry+for+College+Students&rft.pub=Cengage&rft.date=2014-01-01&rft.isbn=9781285965901&rft.aulast=Alexander&rft.aufirst=Daniel+C.&rft.au=Koeberlein%2C+Geralyn+M.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DEN_KAgAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACone" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFHartshorne2013" class="citation book cs1"><a href="/wiki/Robin_Hartshorne" title="Robin Hartshorne">Hartshorne, Robin</a> (2013-11-11). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=C5fSBwAAQBAJ"><i>Geometry: Euclid and Beyond</i></a>. Springer Science & Business Media. Chapter 27. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780387226767" title="Special:BookSources/9780387226767"><bdi>9780387226767</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Geometry%3A+Euclid+and+Beyond&rft.pages=Chapter+27&rft.pub=Springer+Science+%26+Business+Media&rft.date=2013-11-11&rft.isbn=9780387226767&rft.aulast=Hartshorne&rft.aufirst=Robin&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DC5fSBwAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACone" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBlankKrantz2006" class="citation book cs1">Blank, Brian E.; Krantz, Steven George (2006). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=hMY8lbX87Y8C"><i>Calculus: Single Variable</i></a>. Springer. Chapter 8. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781931914598" title="Special:BookSources/9781931914598"><bdi>9781931914598</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Calculus%3A+Single+Variable&rft.pages=Chapter+8&rft.pub=Springer&rft.date=2006&rft.isbn=9781931914598&rft.aulast=Blank&rft.aufirst=Brian+E.&rft.au=Krantz%2C+Steven+George&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DhMY8lbX87Y8C&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACone" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><a href="#CITEREFProtterMorrey1970">Protter & Morrey (1970</a>, p. 583)</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFDowling1917" class="citation book cs1">Dowling, Linnaeus Wayland (1917-01-01). <a rel="nofollow" class="external text" href="https://archive.org/details/projectivegeome04dowlgoog"><i>Projective Geometry</i></a>. McGraw-Hill book Company, Incorporated.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Projective+Geometry&rft.pub=McGraw-Hill+book+Company%2C+Incorporated&rft.date=1917-01-01&rft.aulast=Dowling&rft.aufirst=Linnaeus+Wayland&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fprojectivegeome04dowlgoog&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACone" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><a href="/wiki/G._B._Halsted" title="G. B. Halsted">G. B. Halsted</a> (1906) <i>Synthetic Projective Geometry</i>, page 20</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cone&action=edit&section=16" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFProtterMorrey1970" class="citation cs2">Protter, Murray H.; Morrey, Charles B. Jr. (1970), <i>College Calculus with Analytic Geometry</i> (2nd ed.), Reading: <a href="/wiki/Addison-Wesley" title="Addison-Wesley">Addison-Wesley</a>, <a href="/wiki/LCCN_(identifier)" class="mw-redirect" title="LCCN (identifier)">LCCN</a> <a rel="nofollow" class="external text" href="https://lccn.loc.gov/76087042">76087042</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=College+Calculus+with+Analytic+Geometry&rft.place=Reading&rft.edition=2nd&rft.pub=Addison-Wesley&rft.date=1970&rft_id=info%3Alccn%2F76087042&rft.aulast=Protter&rft.aufirst=Murray+H.&rft.au=Morrey%2C+Charles+B.+Jr.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACone" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cone&action=edit&section=17" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/40px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/60px-Commons-logo.svg.png 1.5x" data-file-width="1024" data-file-height="1376" /></a></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Cones" class="extiw" title="commons:Category:Cones">Cones</a></span>.</div></div> </div> <ul><li><span class="citation mathworld" id="Reference-Mathworld-Cone"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFWeisstein" class="citation web cs1"><a href="/wiki/Eric_W._Weisstein" title="Eric W. Weisstein">Weisstein, Eric W.</a> <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/Cone.html">"Cone"</a>. <i><a href="/wiki/MathWorld" title="MathWorld">MathWorld</a></i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=MathWorld&rft.atitle=Cone&rft.au=Weisstein%2C+Eric+W.&rft_id=https%3A%2F%2Fmathworld.wolfram.com%2FCone.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACone" class="Z3988"></span></span></li> <li><span class="citation mathworld" id="Reference-Mathworld-Double_Cone"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFWeisstein" class="citation web cs1"><a href="/wiki/Eric_W._Weisstein" title="Eric W. Weisstein">Weisstein, Eric W.</a> <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/DoubleCone.html">"Double Cone"</a>. <i><a href="/wiki/MathWorld" title="MathWorld">MathWorld</a></i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=MathWorld&rft.atitle=Double+Cone&rft.au=Weisstein%2C+Eric+W.&rft_id=https%3A%2F%2Fmathworld.wolfram.com%2FDoubleCone.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACone" class="Z3988"></span></span></li> <li><span class="citation mathworld" id="Reference-Mathworld-Generalized_Cone"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFWeisstein" class="citation web cs1"><a href="/wiki/Eric_W._Weisstein" title="Eric W. Weisstein">Weisstein, Eric W.</a> <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/GeneralizedCone.html">"Generalized Cone"</a>. <i><a href="/wiki/MathWorld" title="MathWorld">MathWorld</a></i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=MathWorld&rft.atitle=Generalized+Cone&rft.au=Weisstein%2C+Eric+W.&rft_id=https%3A%2F%2Fmathworld.wolfram.com%2FGeneralizedCone.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACone" class="Z3988"></span></span></li> <li>An interactive <a rel="nofollow" class="external text" href="http://www.mathsisfun.com/geometry/cone.html">Spinning Cone</a> from Maths Is Fun</li> <li><a rel="nofollow" class="external text" href="http://www.korthalsaltes.com/model.php?name_en=cone">Paper model cone</a></li> <li><a rel="nofollow" class="external text" href="http://mathforum.org/library/drmath/view/55017.html">Lateral surface area of an oblique cone</a></li> <li><a rel="nofollow" class="external text" href="http://www.cut-the-knot.org/Curriculum/Geometry/ConicSections.shtml">Cut a Cone</a> An interactive demonstration of the intersection of a cone with a plane</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist 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