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Se mere på \u003Ca href=\"/wiki/Wikipedia:Discord\" title=\"Wikipedia:Discord\"\u003EWikipedia:Discord\u003C/a\u003E\u003C/div\u003E\u003Cp\u003E\u003Ci\u003E\u003Csmall\u003E(\u003Ca href=\"/wiki/Hj%C3%A6lp:Sitenotice\" title=\"Hjælp:Sitenotice\"\u003ELæs her om sitenotice\u003C/a\u003E)\u003C/small\u003E\u003C/i\u003E\u003C/p\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E";}}());</script></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Websted"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Indhold" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Indhold</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">flyt til sidebjælken</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">skjul</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Indledning</div> </a> </li> <li id="toc-Bevis_for_volumen_af_kegle_ved_hjælp_af_omdrejningslegeme_omkring_x-aksen" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bevis_for_volumen_af_kegle_ved_hjælp_af_omdrejningslegeme_omkring_x-aksen"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Bevis for volumen af kegle ved hjælp af omdrejningslegeme omkring x-aksen</span> </div> </a> <ul id="toc-Bevis_for_volumen_af_kegle_ved_hjælp_af_omdrejningslegeme_omkring_x-aksen-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="Indhold" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <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="Vis/skjul indholdsfortegnelsen" > <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">Vis/skjul indholdsfortegnelsen</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">Kegle (geometri)</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="Gå til en artikel på et andet sprog. Tilgængelig på 103 sprog" > <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 sprog</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 – amharisk" lang="am" hreflang="am" data-title="ሾጣጣ" data-language-autonym="አማርኛ" data-language-local-name="amharisk" 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 – arabisk" lang="ar" hreflang="ar" data-title="مخروط" data-language-autonym="العربية" data-language-local-name="arabisk" class="interlanguage-link-target"><span>العربية</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 – aserbajdsjansk" lang="az" hreflang="az" data-title="Konus" data-language-autonym="Azərbaycanca" data-language-local-name="aserbajdsjansk" 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 – balinesisk" lang="ban" hreflang="ban" data-title="Kojong" data-language-autonym="Basa Bali" data-language-local-name="balinesisk" 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 – belarusisk" lang="be" hreflang="be" data-title="Конус" data-language-autonym="Беларуская" data-language-local-name="belarusisk" 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 – bulgarsk" lang="bg" hreflang="bg" data-title="Конус" data-language-autonym="Български" data-language-local-name="bulgarsk" 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) – bosnisk" lang="bs" hreflang="bs" data-title="Kupa (geometrija)" data-language-autonym="Bosanski" data-language-local-name="bosnisk" 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 – catalansk" lang="ca" hreflang="ca" data-title="Con" data-language-autonym="Català" data-language-local-name="catalansk" class="interlanguage-link-target"><span>Català</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-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 – sorani" lang="ckb" hreflang="ckb" data-title="قووچەک" data-language-autonym="کوردی" data-language-local-name="sorani" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Ku%C5%BEel" title="Kužel – tjekkisk" lang="cs" hreflang="cs" data-title="Kužel" data-language-autonym="Čeština" data-language-local-name="tjekkisk" class="interlanguage-link-target"><span>Čeština</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 – tjuvasjisk" lang="cv" hreflang="cv" data-title="Конус" data-language-autonym="Чӑвашла" data-language-local-name="tjuvasjisk" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/C%C3%B4n" title="Côn – walisisk" lang="cy" hreflang="cy" data-title="Côn" data-language-autonym="Cymraeg" data-language-local-name="walisisk" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Kegel_(Geometrie)" title="Kegel (Geometrie) – tysk" lang="de" hreflang="de" data-title="Kegel (Geometrie)" data-language-autonym="Deutsch" data-language-local-name="tysk" class="interlanguage-link-target"><span>Deutsch</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 – græsk" lang="el" hreflang="el" data-title="Κώνος" data-language-autonym="Ελληνικά" data-language-local-name="græsk" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Cone" title="Cone – engelsk" lang="en" hreflang="en" data-title="Cone" data-language-autonym="English" data-language-local-name="engelsk" class="interlanguage-link-target"><span>English</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-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Cono_(geometr%C3%ADa)" title="Cono (geometría) – spansk" lang="es" hreflang="es" data-title="Cono (geometría)" data-language-autonym="Español" data-language-local-name="spansk" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Koonus" title="Koonus – estisk" lang="et" hreflang="et" data-title="Koonus" data-language-autonym="Eesti" data-language-local-name="estisk" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Kono" title="Kono – baskisk" lang="eu" hreflang="eu" data-title="Kono" data-language-autonym="Euskara" data-language-local-name="baskisk" 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 – persisk" lang="fa" hreflang="fa" data-title="مخروط" data-language-autonym="فارسی" data-language-local-name="persisk" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Kartio" title="Kartio – finsk" lang="fi" hreflang="fi" data-title="Kartio" data-language-autonym="Suomi" data-language-local-name="finsk" class="interlanguage-link-target"><span>Suomi</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) – fransk" lang="fr" hreflang="fr" data-title="Cône (géométrie)" data-language-autonym="Français" data-language-local-name="fransk" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Keegel" title="Keegel – nordfrisisk" lang="frr" hreflang="frr" data-title="Keegel" data-language-autonym="Nordfriisk" data-language-local-name="nordfrisisk" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/C%C3%B3n" title="Cón – irsk" lang="ga" hreflang="ga" data-title="Cón" data-language-autonym="Gaeilge" data-language-local-name="irsk" class="interlanguage-link-target"><span>Gaeilge</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-kinesisk" lang="gan" hreflang="gan" data-title="錐形" data-language-autonym="贛語" data-language-local-name="gan-kinesisk" class="interlanguage-link-target"><span>贛語</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-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Cono" title="Cono – galicisk" lang="gl" hreflang="gl" data-title="Cono" data-language-autonym="Galego" data-language-local-name="galicisk" class="interlanguage-link-target"><span>Galego</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-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%97%D7%A8%D7%95%D7%98" title="חרוט – hebraisk" lang="he" hreflang="he" data-title="חרוט" data-language-autonym="עברית" data-language-local-name="hebraisk" class="interlanguage-link-target"><span>עברית</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 – kroatisk" lang="hr" hreflang="hr" data-title="Stožac" data-language-autonym="Hrvatski" data-language-local-name="kroatisk" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/K%C3%BAp" title="Kúp – ungarsk" lang="hu" hreflang="hu" data-title="Kúp" data-language-autonym="Magyar" data-language-local-name="ungarsk" class="interlanguage-link-target"><span>Magyar</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 – armensk" lang="hy" hreflang="hy" data-title="Կոն" data-language-autonym="Հայերեն" data-language-local-name="armensk" class="interlanguage-link-target"><span>Հայերեն</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-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-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Kerucut" title="Kerucut – indonesisk" lang="id" hreflang="id" data-title="Kerucut" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesisk" class="interlanguage-link-target"><span>Bahasa Indonesia</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) – islandsk" lang="is" hreflang="is" data-title="Keila (rúmfræði)" data-language-autonym="Íslenska" data-language-local-name="islandsk" 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 – italiensk" lang="it" hreflang="it" data-title="Cono" data-language-autonym="Italiano" data-language-local-name="italiensk" class="interlanguage-link-target"><span>Italiano</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 – japansk" lang="ja" hreflang="ja" data-title="円錐" data-language-autonym="日本語" data-language-local-name="japansk" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Pasungan" title="Pasungan – javanesisk" lang="jv" hreflang="jv" data-title="Pasungan" data-language-autonym="Jawa" data-language-local-name="javanesisk" class="interlanguage-link-target"><span>Jawa</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 – georgisk" lang="ka" hreflang="ka" data-title="კონუსი" data-language-autonym="ქართული" data-language-local-name="georgisk" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Akawsar_(tusnakt)" title="Akawsar (tusnakt) – kabylsk" lang="kab" hreflang="kab" data-title="Akawsar (tusnakt)" data-language-autonym="Taqbaylit" data-language-local-name="kabylsk" class="interlanguage-link-target"><span>Taqbaylit</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 – kasakhisk" lang="kk" hreflang="kk" data-title="Конус" data-language-autonym="Қазақша" data-language-local-name="kasakhisk" class="interlanguage-link-target"><span>Қазақша</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-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-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9B%90%EB%BF%94" title="원뿔 – koreansk" lang="ko" hreflang="ko" data-title="원뿔" data-language-autonym="한국어" data-language-local-name="koreansk" class="interlanguage-link-target"><span>한국어</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 – kirgisisk" lang="ky" hreflang="ky" data-title="Конус" data-language-autonym="Кыргызча" data-language-local-name="kirgisisk" 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-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-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/K%C5%ABgis" title="Kūgis – litauisk" lang="lt" hreflang="lt" data-title="Kūgis" data-language-autonym="Lietuvių" data-language-local-name="litauisk" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Konuss" title="Konuss – lettisk" lang="lv" hreflang="lv" data-title="Konuss" data-language-autonym="Latviešu" data-language-local-name="lettisk" class="interlanguage-link-target"><span>Latviešu</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-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Kitsoloha" title="Kitsoloha – malagassisk" lang="mg" hreflang="mg" data-title="Kitsoloha" data-language-autonym="Malagasy" data-language-local-name="malagassisk" class="interlanguage-link-target"><span>Malagasy</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 – makedonsk" lang="mk" hreflang="mk" data-title="Конус" data-language-autonym="Македонски" data-language-local-name="makedonsk" class="interlanguage-link-target"><span>Македонски</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-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%83%D1%81" title="Конус – mongolsk" lang="mn" hreflang="mn" data-title="Конус" data-language-autonym="Монгол" data-language-local-name="mongolsk" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Kon" title="Kon – malajisk" lang="ms" hreflang="ms" data-title="Kon" data-language-autonym="Bahasa Melayu" data-language-local-name="malajisk" class="interlanguage-link-target"><span>Bahasa Melayu</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) – nederlandsk" lang="nl" hreflang="nl" data-title="Kegel (ruimtelijke figuur)" data-language-autonym="Nederlands" data-language-local-name="nederlandsk" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Kjegle" title="Kjegle – nynorsk" lang="nn" hreflang="nn" data-title="Kjegle" data-language-autonym="Norsk nynorsk" data-language-local-name="nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Kjegle" title="Kjegle – bokmål" lang="nb" hreflang="nb" data-title="Kjegle" data-language-autonym="Norsk bokmål" data-language-local-name="bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/C%C3%B2n" title="Còn – occitansk" lang="oc" hreflang="oc" data-title="Còn" data-language-autonym="Occitan" data-language-local-name="occitansk" 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Sto%C5%BCek_(bry%C5%82a)" title="Stożek (bryła) – polsk" lang="pl" hreflang="pl" data-title="Stożek (bryła)" data-language-autonym="Polski" data-language-local-name="polsk" class="interlanguage-link-target"><span>Polski</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-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-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Cone" title="Cone – portugisisk" lang="pt" hreflang="pt" data-title="Cone" data-language-autonym="Português" data-language-local-name="portugisisk" class="interlanguage-link-target"><span>Português</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-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Con" title="Con – rumænsk" lang="ro" hreflang="ro" data-title="Con" data-language-autonym="Română" data-language-local-name="rumænsk" class="interlanguage-link-target"><span>Română</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 – russisk" lang="ru" hreflang="ru" data-title="Конус" data-language-autonym="Русский" data-language-local-name="russisk" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Conu" title="Conu – siciliansk" lang="scn" hreflang="scn" data-title="Conu" data-language-autonym="Sicilianu" data-language-local-name="siciliansk" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Sto%C5%BEac" title="Stožac – serbokroatisk" lang="sh" hreflang="sh" data-title="Stožac" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbokroatisk" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</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 – singalesisk" lang="si" hreflang="si" data-title="කේතුව" data-language-autonym="සිංහල" data-language-local-name="singalesisk" 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 – slovakisk" lang="sk" hreflang="sk" data-title="Kužeľ" data-language-autonym="Slovenčina" data-language-local-name="slovakisk" 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 – slovensk" lang="sl" hreflang="sl" data-title="Stožec" data-language-autonym="Slovenščina" data-language-local-name="slovensk" class="interlanguage-link-target"><span>Slovenščina</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-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-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Koni" title="Koni – albansk" lang="sq" hreflang="sq" data-title="Koni" data-language-autonym="Shqip" data-language-local-name="albansk" class="interlanguage-link-target"><span>Shqip</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) – serbisk" lang="sr" hreflang="sr" data-title="Купа (геометрија)" data-language-autonym="Српски / srpski" data-language-local-name="serbisk" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Congcot" title="Congcot – sundanesisk" lang="su" hreflang="su" data-title="Congcot" data-language-autonym="Sunda" data-language-local-name="sundanesisk" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Kon" title="Kon – svensk" lang="sv" hreflang="sv" data-title="Kon" data-language-autonym="Svenska" data-language-local-name="svensk" class="interlanguage-link-target"><span>Svenska</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-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-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-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%83%D1%81" title="Конус – tadsjikisk" lang="tg" hreflang="tg" data-title="Конус" data-language-autonym="Тоҷикӣ" data-language-local-name="tadsjikisk" class="interlanguage-link-target"><span>Тоҷикӣ</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-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-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Koni" title="Koni – tyrkisk" lang="tr" hreflang="tr" data-title="Koni" data-language-autonym="Türkçe" data-language-local-name="tyrkisk" class="interlanguage-link-target"><span>Türkçe</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 – tatarisk" lang="tt" hreflang="tt" data-title="Конус" data-language-autonym="Татарча / tatarça" data-language-local-name="tatarisk" class="interlanguage-link-target"><span>Татарча / tatarça</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 – ukrainsk" lang="uk" hreflang="uk" data-title="Конус" data-language-autonym="Українська" data-language-local-name="ukrainsk" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Konus" title="Konus – usbekisk" lang="uz" hreflang="uz" data-title="Konus" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="usbekisk" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</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 – vietnamesisk" lang="vi" hreflang="vi" data-title="Mặt nón" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamesisk" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link 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class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Udseende</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">flyt til sidebjælken</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">skjul</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" 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">Fra Wikipedia, den frie encyklopædi</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="da" dir="ltr"><dl><dd><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fd/Disambig_bordered_fade.svg/19px-Disambig_bordered_fade.svg.png" decoding="async" width="19" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fd/Disambig_bordered_fade.svg/29px-Disambig_bordered_fade.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fd/Disambig_bordered_fade.svg/38px-Disambig_bordered_fade.svg.png 2x" data-file-width="236" data-file-height="185" /></span></span><i> For alternative betydninger, se <a href="/wiki/Kegle" class="mw-disambig" title="Kegle">Kegle</a>.</i> <small>(<a href="/wiki/Speciel:Pr%C3%A6fiksindeks/Kegle" title="Speciel:Præfiksindeks/Kegle">Se også artikler, som begynder med Kegle</a>)</small></dd></dl> <p>En <b>kegle</b> eller <b>konus</b> er en <a href="/wiki/Geometrisk" class="mw-redirect" title="Geometrisk">geometrisk</a> figur og er illustreret på tegningen til højre side. Fysiske ting som har en form som en matematisk kegle kaldes for <b>kegleformet</b> eller <b>konisk</b>. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fil:Cone_3d.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Cone_3d.png/220px-Cone_3d.png" decoding="async" width="220" height="110" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Cone_3d.png/330px-Cone_3d.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Cone_3d.png/440px-Cone_3d.png 2x" data-file-width="913" data-file-height="458" /></a><figcaption>Kegle</figcaption></figure> <p><br /> <a href="/wiki/Rumfang" title="Rumfang">Rumfanget</a> (Volumen) af en kegle er givet ved </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 V=1/3\cdot \pi \cdot h\cdot r^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> <mo>⋅</mo> <mi>π</mi> <mo>⋅</mo> <mi>h</mi> <mo>⋅</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V=1/3\cdot \pi \cdot h\cdot r^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72934838c89d652e57c9b9fe3ca357cd1b793ddc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.184ex; height:3.176ex;" alt="{\displaystyle V=1/3\cdot \pi \cdot h\cdot r^{2}}"></span></dd></dl> <p>hvor: </p> <ul><li><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> er højden i figuren</li> <li><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> er radius af den cirkulære endeflade.</li></ul> <p><a href="/wiki/Areal" title="Areal">Arealet</a> (overfladen) af en kegle er givet ved </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 A=\pi \cdot r^{2}+\pi \cdot r\cdot s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mo>⋅</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>π</mi> <mo>⋅</mo> <mi>r</mi> <mo>⋅</mo> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=\pi \cdot r^{2}+\pi \cdot r\cdot s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/464b008345bc38c9a893ea071bd5a93458e9293c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:19.625ex; height:2.843ex;" alt="{\displaystyle A=\pi \cdot r^{2}+\pi \cdot r\cdot s}"></span></dd></dl> <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 s={\sqrt {r^{2}+h^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</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 s={\sqrt {r^{2}+h^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7c22336f89fed1ec0807a9c9a31532f656b60bf9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.849ex; height:3.509ex;" alt="{\displaystyle s={\sqrt {r^{2}+h^{2}}}}"></span></dd></dl> <p>hvor: </p> <ul><li><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> er højden i figuren.</li> <li><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> er radius af den cirkulære endeflade.</li> <li><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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span> er hypotenusen i trekanten med kateterne <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> og <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>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Bevis_for_volumen_af_kegle_ved_hjælp_af_omdrejningslegeme_omkring_x-aksen"><span id="Bevis_for_volumen_af_kegle_ved_hj.C3.A6lp_af_omdrejningslegeme_omkring_x-aksen"></span>Bevis for volumen af kegle ved hjælp af omdrejningslegeme omkring x-aksen</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kegle_(geometri)&veaction=edit&section=1" title="Redigér afsnit: Bevis for volumen af kegle ved hjælp af omdrejningslegeme omkring x-aksen" class="mw-editsection-visualeditor"><span>redigér</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kegle_(geometri)&action=edit&section=1" title="Edit section's source code: Bevis for volumen af kegle ved hjælp af omdrejningslegeme omkring x-aksen"><span>rediger kildetekst</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Beviset tager udgangspunkt i volumen af omdrejningslegeme omkring x-aksen. Beviset ses herunder, og forløber således: der findes et andet udtryk for hældningen (a) </p><p>i den rette linje (f(x)), som har en b-værdi på 0, da den skærer y-aksen i origo (0,0). Herefter indsættes funktionen i udtrykket for volumen af omdrejningslegeme omkring </p><p>x-aksen. Da r og h er konstanter, kan denne brøk sættes ud foran integraltegnet, og vi kan nu hæve integraltegnet ved at integerere x kvadreret, og indsætte grænserne </p><p>som er fra 0 til h, som kan ses på skitsen. Herefter forkortes vores udtryk, og vi har nu bevist volumen af en kegle. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fil:Volumen_af_kegle_skitse.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Volumen_af_kegle_skitse.png/220px-Volumen_af_kegle_skitse.png" decoding="async" width="220" height="185" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/2/22/Volumen_af_kegle_skitse.png 1.5x" data-file-width="279" data-file-height="235" /></a><figcaption>Skitse til bevist (funktionen omdrejes 360 grader om x-aksen)</figcaption></figure> <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 {\begin{aligned}&f(x)=ax\\&a={\frac {\Delta y}{\Delta x}}={\frac {r}{h}}\\&f(x)={\frac {r}{h}}\cdot x\\&V=\pi \cdot \int _{0}^{h}\left({\frac {r}{h}}\cdot x\right)^{2}dx\\&V=\pi \cdot {\frac {r^{2}}{h^{2}}}\cdot \int _{0}^{h}x^{2}dx\\&V=\pi \cdot {\frac {r^{2}}{h^{2}}}\cdot {\frac {1}{3}}\cdot h^{3}\\&V={\frac {1}{3}}\cdot \pi \cdot h\cdot r^{2}\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd /> <mtd> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>a</mi> <mi>x</mi> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi>a</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>y</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>r</mi> <mi>h</mi> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>r</mi> <mi>h</mi> </mfrac> </mrow> <mo>⋅</mo> <mi>x</mi> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi>V</mi> <mo>=</mo> <mi>π</mi> <mo>⋅</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> </msubsup> <msup> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>r</mi> <mi>h</mi> </mfrac> </mrow> <mo>⋅</mo> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>d</mi> <mi>x</mi> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi>V</mi> <mo>=</mo> <mi>π</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>⋅</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> </msubsup> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>d</mi> <mi>x</mi> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi>V</mi> <mo>=</mo> <mi>π</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> </mrow> <mo>⋅</mo> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi>V</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> </mrow> <mo>⋅</mo> <mi>π</mi> <mo>⋅</mo> <mi>h</mi> <mo>⋅</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}&f(x)=ax\\&a={\frac {\Delta y}{\Delta x}}={\frac {r}{h}}\\&f(x)={\frac {r}{h}}\cdot x\\&V=\pi \cdot \int _{0}^{h}\left({\frac {r}{h}}\cdot x\right)^{2}dx\\&V=\pi \cdot {\frac {r^{2}}{h^{2}}}\cdot \int _{0}^{h}x^{2}dx\\&V=\pi \cdot {\frac {r^{2}}{h^{2}}}\cdot {\frac {1}{3}}\cdot h^{3}\\&V={\frac {1}{3}}\cdot \pi \cdot h\cdot r^{2}\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/758f1b17033819ebf1329e5594307d42f3a805dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -18.272ex; margin-bottom: -0.233ex; width:24.238ex; height:38.176ex;" alt="{\displaystyle {\begin{aligned}&f(x)=ax\\&a={\frac {\Delta y}{\Delta x}}={\frac {r}{h}}\\&f(x)={\frac {r}{h}}\cdot x\\&V=\pi \cdot \int _{0}^{h}\left({\frac {r}{h}}\cdot x\right)^{2}dx\\&V=\pi \cdot {\frac {r^{2}}{h^{2}}}\cdot \int _{0}^{h}x^{2}dx\\&V=\pi \cdot {\frac {r^{2}}{h^{2}}}\cdot {\frac {1}{3}}\cdot h^{3}\\&V={\frac {1}{3}}\cdot \pi \cdot h\cdot r^{2}\end{aligned}}}"></span></dd></dl> <table class="infobox sisterproject"> <tbody><tr> <td style="width:50px; height:67px;"><figure class="mw-halign-none" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/50px-Commons-logo.svg.png" decoding="async" width="50" height="67" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/75px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/100px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span><figcaption></figcaption></figure> </td> <td style="padding-left:5px;"><a href="https://commons.wikimedia.org/wiki/Forside" class="extiw" title="commons:Forside">Wikimedia Commons</a> har medier relateret til: <div style="margin-left: 10px;"> <i><b><a href="https://commons.wikimedia.org/wiki/Category:Cones" class="extiw" 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