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class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">déplacer vers la barre latérale</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">masquer</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">Début</div> </a> </li> <li id="toc-Surface" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Surface"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Surface</span> </div> </a> <button aria-controls="toc-Surface-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>Afficher / masquer la sous-section Surface</span> </button> <ul id="toc-Surface-sublist" class="vector-toc-list"> <li id="toc-Cas_général" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cas_général"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Cas général</span> </div> </a> <ul id="toc-Cas_général-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cône_de_révolution" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cône_de_révolution"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Cône de révolution</span> </div> </a> <ul id="toc-Cône_de_révolution-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sections_d'un_cône_de_révolution_par_un_plan" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sections_d'un_cône_de_révolution_par_un_plan"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Sections d'un cône de révolution par un plan</span> </div> </a> <ul id="toc-Sections_d'un_cône_de_révolution_par_un_plan-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Solide" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Solide"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Solide</span> </div> </a> <button aria-controls="toc-Solide-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>Afficher / masquer la sous-section Solide</span> </button> <ul id="toc-Solide-sublist" class="vector-toc-list"> <li id="toc-Cas_général_2" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cas_général_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Cas général</span> </div> </a> <ul id="toc-Cas_général_2-sublist" class="vector-toc-list"> <li id="toc-Volume" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Volume"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.1</span> <span>Volume</span> </div> </a> <ul id="toc-Volume-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cône_tronqué" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Cône_tronqué"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.2</span> <span>Cône tronqué</span> </div> </a> <ul id="toc-Cône_tronqué-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Cas_du_cône_de_révolution" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cas_du_cône_de_révolution"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Cas du cône de révolution</span> </div> </a> <ul id="toc-Cas_du_cône_de_révolution-sublist" class="vector-toc-list"> <li id="toc-Aire_latérale" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Aire_latérale"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.1</span> <span>Aire latérale</span> </div> </a> <ul id="toc-Aire_latérale-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Section_du_cône_de_révolution_par_un_plan" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Section_du_cône_de_révolution_par_un_plan"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.2</span> <span>Section du cône de révolution par un plan</span> </div> </a> <ul id="toc-Section_du_cône_de_révolution_par_un_plan-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Patron_ou_développement_d'un_cône_de_révolution" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Patron_ou_développement_d'un_cône_de_révolution"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.3</span> <span>Patron ou développement d'un cône de révolution</span> </div> </a> <ul id="toc-Patron_ou_développement_d'un_cône_de_révolution-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Notes_et_références" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes_et_références"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Notes et références</span> </div> </a> <ul id="toc-Notes_et_références-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Voir_aussi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Voir_aussi"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Voir aussi</span> </div> </a> <button aria-controls="toc-Voir_aussi-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>Afficher / masquer la sous-section Voir aussi</span> </button> <ul id="toc-Voir_aussi-sublist" class="vector-toc-list"> <li id="toc-Bibliographie" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bibliographie"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Bibliographie</span> </div> </a> <ul id="toc-Bibliographie-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Articles_connexes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Articles_connexes"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Articles connexes</span> </div> </a> <ul id="toc-Articles_connexes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Liens_externes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Liens_externes"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Liens externes</span> </div> </a> <ul id="toc-Liens_externes-sublist" class="vector-toc-list"> </ul> </li> </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="Sommaire" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table des matières" > <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="Basculer la table des matières" > <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">Basculer la table des matières</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">Cône (géométrie)</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="Aller à un article dans une autre langue. Disponible en 103 langues." > <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 langues</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 – amharique" lang="am" hreflang="am" data-title="ሾጣጣ" data-language-autonym="አማርኛ" data-language-local-name="amharique" 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 – arabe" lang="ar" hreflang="ar" data-title="مخروط" data-language-autonym="العربية" data-language-local-name="arabe" 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 – azerbaïdjanais" lang="az" hreflang="az" data-title="Konus" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaïdjanais" 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 – balinais" lang="ban" hreflang="ban" data-title="Kojong" data-language-autonym="Basa Bali" data-language-local-name="balinais" 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 – biélorusse" lang="be" hreflang="be" data-title="Конус" data-language-autonym="Беларуская" data-language-local-name="biélorusse" 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 – bulgare" lang="bg" hreflang="bg" data-title="Конус" data-language-autonym="Български" data-language-local-name="bulgare" 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) – bosniaque" lang="bs" hreflang="bs" data-title="Kupa (geometrija)" data-language-autonym="Bosanski" data-language-local-name="bosniaque" 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-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 – tchèque" lang="cs" hreflang="cs" data-title="Kužel" data-language-autonym="Čeština" data-language-local-name="tchèque" 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 – tchouvache" lang="cv" hreflang="cv" data-title="Конус" data-language-autonym="Чӑвашла" data-language-local-name="tchouvache" 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 – gallois" lang="cy" hreflang="cy" data-title="Côn" data-language-autonym="Cymraeg" data-language-local-name="gallois" 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) – danois" lang="da" hreflang="da" data-title="Kegle (geometri)" data-language-autonym="Dansk" data-language-local-name="danois" 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) – allemand" lang="de" hreflang="de" data-title="Kegel (Geometrie)" data-language-autonym="Deutsch" data-language-local-name="allemand" 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 – grec" lang="el" hreflang="el" data-title="Κώνος" data-language-autonym="Ελληνικά" data-language-local-name="grec" 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 – anglais" lang="en" hreflang="en" data-title="Cone" data-language-autonym="English" data-language-local-name="anglais" 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 – espéranto" lang="eo" hreflang="eo" data-title="Konuso" data-language-autonym="Esperanto" data-language-local-name="espéranto" 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) – espagnol" lang="es" hreflang="es" data-title="Cono (geometría)" data-language-autonym="Español" data-language-local-name="espagnol" 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 – estonien" lang="et" hreflang="et" data-title="Koonus" data-language-autonym="Eesti" data-language-local-name="estonien" 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 – 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 – persan" lang="fa" hreflang="fa" data-title="مخروط" data-language-autonym="فارسی" data-language-local-name="persan" 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 – finnois" lang="fi" hreflang="fi" data-title="Kartio" data-language-autonym="Suomi" data-language-local-name="finnois" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Keegel" title="Keegel – frison septentrional" lang="frr" hreflang="frr" data-title="Keegel" data-language-autonym="Nordfriisk" data-language-local-name="frison septentrional" 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 – irlandais" lang="ga" hreflang="ga" data-title="Cón" data-language-autonym="Gaeilge" data-language-local-name="irlandais" 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" 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-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Konik" title="Konik – créole guyanais" lang="gcr" hreflang="gcr" data-title="Konik" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="créole guyanais" 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 – galicien" lang="gl" hreflang="gl" data-title="Cono" data-language-autonym="Galego" data-language-local-name="galicien" 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 – goudjarati" lang="gu" hreflang="gu" data-title="શંકુ" data-language-autonym="ગુજરાતી" data-language-local-name="goudjarati" 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 – hébreu" lang="he" hreflang="he" data-title="חרוט" data-language-autonym="עברית" data-language-local-name="hébreu" 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 – croate" lang="hr" hreflang="hr" data-title="Stožac" data-language-autonym="Hrvatski" data-language-local-name="croate" 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 – hongrois" lang="hu" hreflang="hu" data-title="Kúp" data-language-autonym="Magyar" data-language-local-name="hongrois" 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 – arménien" lang="hy" hreflang="hy" data-title="Կոն" data-language-autonym="Հայերեն" data-language-local-name="arménien" 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 – arménien occidental" lang="hyw" hreflang="hyw" data-title="Քոն" data-language-autonym="Արեւմտահայերէն" data-language-local-name="arménien occidental" 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 – indonésien" lang="id" hreflang="id" data-title="Kerucut" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonésien" 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) – islandais" lang="is" hreflang="is" data-title="Keila (rúmfræði)" data-language-autonym="Íslenska" data-language-local-name="islandais" 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 – italien" lang="it" hreflang="it" data-title="Cono" data-language-autonym="Italiano" data-language-local-name="italien" 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 – japonais" lang="ja" hreflang="ja" data-title="円錐" data-language-autonym="日本語" data-language-local-name="japonais" 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 – javanais" lang="jv" hreflang="jv" data-title="Pasungan" data-language-autonym="Jawa" data-language-local-name="javanais" 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 – géorgien" lang="ka" hreflang="ka" data-title="კონუსი" data-language-autonym="ქართული" data-language-local-name="géorgien" 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) – 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-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-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 – coréen" lang="ko" hreflang="ko" data-title="원뿔" data-language-autonym="한국어" data-language-local-name="coréen" 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 – kirghize" lang="ky" hreflang="ky" data-title="Конус" data-language-autonym="Кыргызча" data-language-local-name="kirghize" 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 – lituanien" lang="lt" hreflang="lt" data-title="Kūgis" data-language-autonym="Lietuvių" data-language-local-name="lituanien" 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 – letton" lang="lv" hreflang="lv" data-title="Konuss" data-language-autonym="Latviešu" data-language-local-name="letton" 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 – mokcha" lang="mdf" hreflang="mdf" data-title="Конуссь" data-language-autonym="Мокшень" data-language-local-name="mokcha" 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 – malgache" lang="mg" hreflang="mg" data-title="Kitsoloha" data-language-autonym="Malagasy" data-language-local-name="malgache" 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 – macédonien" lang="mk" hreflang="mk" data-title="Конус" data-language-autonym="Македонски" data-language-local-name="macédonien" 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 – mongol" lang="mn" hreflang="mn" data-title="Конус" data-language-autonym="Монгол" data-language-local-name="mongol" 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 – malais" lang="ms" hreflang="ms" data-title="Kon" data-language-autonym="Bahasa Melayu" data-language-local-name="malais" 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) – néerlandais" lang="nl" hreflang="nl" data-title="Kegel (ruimtelijke figuur)" data-language-autonym="Nederlands" data-language-local-name="néerlandais" 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 – norvégien nynorsk" lang="nn" hreflang="nn" data-title="Kjegle" data-language-autonym="Norsk nynorsk" data-language-local-name="norvégien 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 – norvégien bokmål" lang="nb" hreflang="nb" data-title="Kjegle" data-language-autonym="Norsk bokmål" data-language-local-name="norvégien 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 – 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Sto%C5%BCek_(bry%C5%82a)" title="Stożek (bryła) – polonais" lang="pl" hreflang="pl" data-title="Stożek (bryła)" data-language-autonym="Polski" data-language-local-name="polonais" 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 – piémontais" lang="pms" hreflang="pms" data-title="Còno" data-language-autonym="Piemontèis" data-language-local-name="piémontais" 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 – pachto" lang="ps" hreflang="ps" data-title="بوکر" data-language-autonym="پښتو" data-language-local-name="pachto" 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 – portugais" lang="pt" hreflang="pt" data-title="Cone" data-language-autonym="Português" data-language-local-name="portugais" 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 – roumain" lang="ro" hreflang="ro" data-title="Con" data-language-autonym="Română" data-language-local-name="roumain" 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 – russe" lang="ru" hreflang="ru" data-title="Конус" data-language-autonym="Русский" data-language-local-name="russe" 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 – sicilien" lang="scn" hreflang="scn" data-title="Conu" data-language-autonym="Sicilianu" data-language-local-name="sicilien" 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 – serbo-croate" lang="sh" hreflang="sh" data-title="Stožac" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbo-croate" 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 – cingalais" lang="si" hreflang="si" data-title="කේතුව" data-language-autonym="සිංහල" data-language-local-name="cingalais" 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 – slovaque" lang="sk" hreflang="sk" data-title="Kužeľ" data-language-autonym="Slovenčina" data-language-local-name="slovaque" 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 – slovène" lang="sl" hreflang="sl" data-title="Stožec" data-language-autonym="Slovenščina" data-language-local-name="slovène" 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 – albanais" lang="sq" hreflang="sq" data-title="Koni" data-language-autonym="Shqip" data-language-local-name="albanais" 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) – serbe" lang="sr" hreflang="sr" data-title="Купа (геометрија)" data-language-autonym="Српски / srpski" data-language-local-name="serbe" 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 – soundanais" lang="su" hreflang="su" data-title="Congcot" data-language-autonym="Sunda" data-language-local-name="soundanais" 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 – suédois" lang="sv" hreflang="sv" data-title="Kon" data-language-autonym="Svenska" data-language-local-name="suédois" 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 – tamoul" lang="ta" hreflang="ta" data-title="கூம்பு" data-language-autonym="தமிழ்" data-language-local-name="tamoul" 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 – télougou" lang="te" hreflang="te" data-title="శంకువు" data-language-autonym="తెలుగు" data-language-local-name="télougou" 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 – tadjik" lang="tg" hreflang="tg" data-title="Конус" data-language-autonym="Тоҷикӣ" data-language-local-name="tadjik" 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 – thaï" lang="th" hreflang="th" data-title="ทรงกรวย" data-language-autonym="ไทย" data-language-local-name="thaï" 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 – turc" lang="tr" hreflang="tr" data-title="Koni" data-language-autonym="Türkçe" data-language-local-name="turc" 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 – 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-tyv mw-list-item"><a href="https://tyv.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%83%D1%81" title="Конус – touvain" lang="tyv" hreflang="tyv" data-title="Конус" data-language-autonym="Тыва дыл" data-language-local-name="touvain" 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 – ukrainien" lang="uk" hreflang="uk" data-title="Конус" data-language-autonym="Українська" data-language-local-name="ukrainien" 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 – ouzbek" lang="uz" hreflang="uz" data-title="Konus" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="ouzbek" 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 – vietnamien" lang="vi" hreflang="vi" data-title="Mặt nón" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamien" 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 mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%9C%86%E9%94%A5" title="圆锥 – chinois" lang="zh" hreflang="zh" data-title="圆锥" data-language-autonym="中文" data-language-local-name="chinois" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%9C%93%E9%8C%90" title="圓錐 – cantonais" lang="yue" hreflang="yue" data-title="圓錐" data-language-autonym="粵語" data-language-local-name="cantonais" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q42344#sitelinks-wikipedia" title="Modifier les liens interlangues" class="wbc-editpage">Modifier les liens</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Espaces de noms"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/C%C3%B4ne_(g%C3%A9om%C3%A9trie)" title="Voir le contenu de la page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Discussion:C%C3%B4ne_(g%C3%A9om%C3%A9trie)" rel="discussion" title="Discussion au sujet de cette page de contenu [t]" accesskey="t"><span>Discussion</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" 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href="/wiki/C%C3%B4ne_(g%C3%A9om%C3%A9trie)"><span>Lire</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&veaction=edit" title="Modifier cette page [v]" accesskey="v"><span>Modifier</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&action=edit" title="Modifier le wikicode de cette page [e]" accesskey="e"><span>Modifier le code</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&action=history" title="Historique des versions de cette page [h]" accesskey="h"><span>Voir l’historique</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Outils de la page"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" 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<div class="vector-pinnable-header-label">Outils</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">déplacer vers la barre latérale</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">masquer</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Plus d’options" > <div class="vector-menu-heading"> Actions </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/C%C3%B4ne_(g%C3%A9om%C3%A9trie)"><span>Lire</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&veaction=edit" title="Modifier cette page [v]" accesskey="v"><span>Modifier</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&action=edit" title="Modifier le wikicode de cette page [e]" accesskey="e"><span>Modifier le code</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&action=history"><span>Voir l’historique</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Général </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Sp%C3%A9cial:Pages_li%C3%A9es/C%C3%B4ne_(g%C3%A9om%C3%A9trie)" title="Liste des pages liées qui pointent sur celle-ci [j]" accesskey="j"><span>Pages liées</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Sp%C3%A9cial:Suivi_des_liens/C%C3%B4ne_(g%C3%A9om%C3%A9trie)" rel="nofollow" title="Liste des modifications récentes des pages appelées par celle-ci [k]" accesskey="k"><span>Suivi des pages liées</span></a></li><li id="t-upload" class="mw-list-item"><a href="//fr.wikipedia.org/wiki/Aide:Importer_un_fichier" title="Téléverser des fichiers [u]" accesskey="u"><span>Téléverser un fichier</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&oldid=219432053" title="Adresse permanente de cette version de cette page"><span>Lien permanent</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&action=info" title="Davantage d’informations sur cette page"><span>Informations sur la page</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Sp%C3%A9cial:Citer&page=C%C3%B4ne_%28g%C3%A9om%C3%A9trie%29&id=219432053&wpFormIdentifier=titleform" title="Informations sur la manière de citer cette page"><span>Citer cette page</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Sp%C3%A9cial:UrlShortener&url=https%3A%2F%2Ffr.wikipedia.org%2Fwiki%2FC%25C3%25B4ne_%28g%25C3%25A9om%25C3%25A9trie%29"><span>Obtenir l'URL raccourcie</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Sp%C3%A9cial:QrCode&url=https%3A%2F%2Ffr.wikipedia.org%2Fwiki%2FC%25C3%25B4ne_%28g%25C3%25A9om%25C3%25A9trie%29"><span>Télécharger le code QR</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Imprimer / exporter </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Sp%C3%A9cial:Livre&bookcmd=book_creator&referer=C%C3%B4ne+%28g%C3%A9om%C3%A9trie%29"><span>Créer un livre</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Sp%C3%A9cial:DownloadAsPdf&page=C%C3%B4ne_%28g%C3%A9om%C3%A9trie%29&action=show-download-screen"><span>Télécharger comme PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&printable=yes" title="Version imprimable de cette page [p]" accesskey="p"><span>Version imprimable</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> Dans d’autres projets </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Cones" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q42344" title="Lien vers l’élément dans le dépôt de données connecté [g]" accesskey="g"><span>Élément Wikidata</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Outils de la page"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Apparence"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" 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">Apparence</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">déplacer vers la barre latérale</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">masquer</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">Un article de Wikipédia, l'encyclopédie libre.</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="fr" dir="ltr"><div class="bandeau-container metadata homonymie hatnote"><div class="bandeau-cell bandeau-icone" style="display:table-cell;padding-right:0.5em"><span class="noviewer" typeof="mw:File"><a href="/wiki/Aide:Homonymie" title="Aide:Homonymie"><img alt="Page d’aide sur l’homonymie" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Logo_disambig.svg/20px-Logo_disambig.svg.png" decoding="async" width="20" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Logo_disambig.svg/30px-Logo_disambig.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Logo_disambig.svg/40px-Logo_disambig.svg.png 2x" data-file-width="512" data-file-height="375" /></a></span></div><div class="bandeau-cell" style="display:table-cell;padding-right:0.5em"> <p>Pour les articles homonymes, voir <a href="/wiki/C%C3%B4ne" class="mw-disambig" title="Cône">Cône</a> (inclut d'autres significations mathématiques). </p> </div></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fichier: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 à l'article <i>Problemata mathematica...</i> publiée sur les <a href="/wiki/Acta_Eruditorum" title="Acta Eruditorum">Acta Eruditorum</a>, 1734</figcaption></figure> <p>En <a href="/wiki/G%C3%A9om%C3%A9trie" title="Géométrie">géométrie</a>, un <b>cône</b> est une <a href="/wiki/Surface_r%C3%A9gl%C3%A9e" title="Surface réglée">surface réglée</a> ou bien un <a href="/wiki/Solide_g%C3%A9om%C3%A9trique" title="Solide géométrique">solide</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Surface">Surface</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&veaction=edit&section=1" title="Modifier la section : Surface" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&action=edit&section=1" title="Modifier le code source de la section : Surface"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Cas_général"><span id="Cas_g.C3.A9n.C3.A9ral"></span>Cas général</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&veaction=edit&section=2" title="Modifier la section : Cas général" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&action=edit&section=2" title="Modifier le code source de la section : Cas général"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File"><a href="/wiki/Fichier:Cones_geometrie.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Cones_geometrie.png" decoding="async" width="327" height="432" class="mw-file-element" data-file-width="327" data-file-height="432" /></a><figcaption></figcaption></figure> <p>Un cône est une <a href="/wiki/Surface_r%C3%A9gl%C3%A9e" title="Surface réglée">surface réglée</a> définie par une <a href="/wiki/Droite_(math%C3%A9matiques)" title="Droite (mathématiques)">droite</a> (<i>d</i>), appelée <i><a href="/wiki/G%C3%A9n%C3%A9ratrice_(math%C3%A9matiques)" title="Génératrice (mathématiques)">génératrice</a></i>, passant par un point fixe <i>S</i> appelé <i>sommet</i> et un point variable décrivant une <a href="/wiki/Courbe_plane" title="Courbe plane">courbe</a> (<i>c</i>), appelée <i>courbe <a href="/wiki/Directrice_(math%C3%A9matiques)" title="Directrice (mathématiques)">directrice</a></i>. </p><p>On parle aussi dans ce cas de <b>surface conique</b>. </p> <div class="mw-heading mw-heading3"><h3 id="Cône_de_révolution"><span id="C.C3.B4ne_de_r.C3.A9volution"></span>Cône de révolution</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&veaction=edit&section=3" title="Modifier la section : Cône de révolution" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&action=edit&section=3" title="Modifier le code source de la section : Cône de révolution"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="bandeau-container bandeau-section metadata bandeau-niveau-information"><div class="bandeau-cell bandeau-icone-css loupe">Article détaillé : <a href="/wiki/C%C3%B4ne_de_r%C3%A9volution" title="Cône de révolution">Cône de révolution</a>.</div></div> <p>Parmi ces surfaces coniques, la plus étudiée est le cône de <a href="/wiki/Surface_de_r%C3%A9volution" title="Surface de révolution">révolution</a> dans lequel la courbe directrice est un cercle de centre O situé dans un plan perpendiculaire à (SO). Ce cône est appelé de révolution car il peut être généré simplement par la rotation d'une droite (d) passant par S autour d'un axe (Sz) différent de (d). La génératrice du cône fait alors un angle fixe <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 \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }" /></span> avec l'axe de rotation. </p><p>C'est à partir de ce cône de révolution que les mathématiciens (dont <a href="/wiki/Apollonius_de_Perga" class="mw-redirect" title="Apollonius de Perga">Apollonius de Perga</a>) ont classifié un ensemble de courbes comme des <a href="/wiki/Conique" title="Conique">coniques</a> (intersection du cône et d'un plan) : <a href="/wiki/Cercle" title="Cercle">cercles</a>, <a href="/wiki/Ellipse_(math%C3%A9matiques)" title="Ellipse (mathématiques)">ellipses</a>, <a href="/wiki/Parabole" title="Parabole">paraboles</a>, <a href="/wiki/Hyperbole_(math%C3%A9matiques)" title="Hyperbole (mathématiques)">hyperboles</a>. </p><p>Dans le repère orthonormal (<i>S</i>, <i>i</i>, <i>j</i>, <i>k</i>), l'équation du cône de révolution d'axe (<i>Sz</i>) et de sommet <i>S</i> est donnée par : </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 x^{2}+y^{2}=z^{2}(\tan \ \alpha )^{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> <mo stretchy="false">(</mo> <mi>tan</mi> <mo>⁡</mo> <mtext> </mtext> <mi>α</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}+y^{2}=z^{2}(\tan \ \alpha )^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2412b34064c49a406864db116941ffdbadc8f3fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.361ex; height:3.176ex;" alt="{\displaystyle x^{2}+y^{2}=z^{2}(\tan \ \alpha )^{2}}" /></span></dd></dl> <p>où <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 \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }" /></span> est l'angle du cône (ou demi-angle au sommet), formé par l'axe de révolution et une génératrice. </p> <div class="clear" style="clear:both;"></div> <div class="mw-heading mw-heading3"><h3 id="Sections_d'un_cône_de_révolution_par_un_plan"><span id="Sections_d.27un_c.C3.B4ne_de_r.C3.A9volution_par_un_plan"></span>Sections d'un cône de révolution par un plan</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&veaction=edit&section=4" title="Modifier la section : Sections d'un cône de révolution par un plan" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&action=edit&section=4" title="Modifier le code source de la section : Sections d'un cône de révolution par un plan"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fichier:Coniques_cone.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Coniques_cone.png/440px-Coniques_cone.png" decoding="async" width="440" height="275" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/5/51/Coniques_cone.png 1.5x" data-file-width="536" data-file-height="335" /></a><figcaption>Intersection d'un plan et d'un cône de révolution.</figcaption></figure> <p>Dans les cas où le plan est parallèle ou perpendiculaire à l'axe de révolution du cône on obtient les courbes suivantes : </p> <ul><li>La section d'un cône de révolution par un plan perpendiculaire à l'axe de révolution est un cercle.</li> <li>La section d'un cône de révolution par un plan parallèle à l'axe de révolution est <ul><li>l'union de deux droites sécantes si le plan contient l'axe de révolution</li> <li>une hyperbole dans le cas contraire</li></ul></li></ul> <p>Plus généralement, la section d'un cône de révolution par un plan donne une <a href="/wiki/Conique" title="Conique">conique</a>. Ainsi on trouve, </p> <ul><li>une <a href="/wiki/Parabole" title="Parabole">parabole</a> (réduite éventuellement à une génératrice) lorsque le plan est strictement parallèle à une génératrice du cône</li> <li>une <a href="/wiki/Ellipse_(math%C3%A9matiques)" title="Ellipse (mathématiques)">ellipse</a> (éventuellement réduite à un point) quand l'angle que forme le vecteur normal au plan et l'axe de rotation est inférieur à π/2 - α</li> <li>une <a href="/wiki/Hyperbole_(math%C3%A9matiques)" title="Hyperbole (mathématiques)">hyperbole</a> (éventuellement réduite à deux droites sécantes) quand l'angle que forme le vecteur normal au plan et l'axe de rotation est supérieur à π/2 - α</li></ul> <div class="mw-heading mw-heading2"><h2 id="Solide">Solide</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&veaction=edit&section=5" title="Modifier la section : Solide" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&action=edit&section=5" title="Modifier le code source de la section : Solide"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Cas_général_2"><span id="Cas_g.C3.A9n.C3.A9ral_2"></span>Cas général</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&veaction=edit&section=6" title="Modifier la section : Cas général" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&action=edit&section=6" title="Modifier le code source de la section : Cas général"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Fichier: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>Cône de révolution et cône quelconque.</figcaption></figure> <p>On appelle aussi <b>cône</b> le <a href="/wiki/Solide_g%C3%A9om%C3%A9trique" title="Solide géométrique">solide</a> délimité par la surface conique, le sommet <i>S</i> et un plan (<i>P</i>) ne contenant pas <i>S</i> et sécant à toutes les génératrices. La section du plan et de la surface s'appelle la <i>base</i> du cône. </p><p>Lorsque la section est circulaire de centre <i>O</i> et que la droite (<i>OS</i>) est perpendiculaire à la section, le cône est appelé <b>cône de révolution</b> ou <b>cône circulaire droit</b>. C'est le cône le plus connu (<a href="/wiki/Cornet_de_glace" class="mw-redirect" title="Cornet de glace">cornet de glace</a>, <a href="/wiki/Chapeau" title="Chapeau">chapeau de clown</a>). Dans ce cas, la distance séparant le sommet d'un point quelconque du cercle est constante et s'appelle l'<i><a href="/wiki/Apoth%C3%A8me" title="Apothème">apothème</a></i> du cône. </p><p>Lorsque la courbe fermée est un <a href="/wiki/Polygone" title="Polygone">polygone</a>, on obtient une <a href="/wiki/Pyramide" title="Pyramide">pyramide</a>. </p> <div class="mw-heading mw-heading4"><h4 id="Volume">Volume</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&veaction=edit&section=7" title="Modifier la section : Volume" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&action=edit&section=7" title="Modifier le code source de la section : Volume"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="bandeau-container bandeau-section metadata bandeau-niveau-information"><div class="bandeau-cell bandeau-icone-css loupe">Articles détaillés : <a href="/wiki/M%C3%A9thode_des_indivisibles#Calculs_de_volumes" title="Méthode des indivisibles">Méthode des indivisibles</a> et <a href="/wiki/M%C3%A9thode_d%27exhaustion#Volume_de_la_pyramide_et_du_cône" title="Méthode d'exhaustion">Méthode d'exhaustion</a>.</div></div> <p>Quelle que soit la forme du cône, son <a href="/wiki/Volume" title="Volume">volume</a> est toujours le tiers du volume d'un <a href="/wiki/Cylindre_(solide)" class="mw-redirect" title="Cylindre (solide)">cylindre</a> de mêmes base et hauteur : </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={\frac {1}{3}}B\times 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>B</mi> <mo>×</mo> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V={\frac {1}{3}}B\times h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d275aeb2718496f110b49297c0b163dfed31f32b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.828ex; height:5.176ex;" alt="{\displaystyle V={\frac {1}{3}}B\times h}" /></span></dd></dl> <p>où <i>B</i> est l'<a href="/wiki/Aire_(g%C3%A9om%C3%A9trie)" title="Aire (géométrie)">aire</a> de la base et <i>h</i> la hauteur du cône, c'est-à-dire la distance séparant le sommet <i>S</i> et le plan (<i>P</i>). </p> <div class="NavFrame" style="border: thin solid #aaaaaa; margin:1em 2em; padding: 0 1em; font-size:100%; text-align:justify; overflow:hidden;"> <div class="NavHead" style="background-color:transparent; color:inherit; padding:0;">Démonstration</div><div class="NavContent" style="padding-bottom:0.4em"> <p>Les dimensions d'une section plane parallèle à la base augmentent de façon linéaire à partir du sommet <i>S</i> vers la base. La section plane, à une distance quelconque <i>y</i> de <i>S</i>, est la base mise à l'échelle par un facteur de <i>y</i>/<i>h</i>, où <i>h</i> est la distance entre <i>S</i> et la base. Puisque l'aire d'une forme quelconque est multipliée <span class="need_ref" title="Je comprends la démonstration, mais je ne comprends pas trop cette phrase, qui ne me semble pas claire." style="cursor:help;">par le carré de la forme mise à l'échelle</span><sup class="need_ref_tag" style="padding-left:2px;"><a href="/wiki/Wikip%C3%A9dia:Style_encyclop%C3%A9dique#Clair" title="Wikipédia:Style encyclopédique">[pas clair]</a></sup>, l'aire de la section plane à une distance <i>y</i> de <i>S</i> est <i>By</i><sup>2</sup>/<i>h</i><sup>2</sup>. </p><p>Le volume est donné par l'intégrale </p><p><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 {B}{h^{2}}}\int _{0}^{h}y^{2}{\rm {d}}y={\frac {B}{h^{2}}}\left[{\frac {y^{3}}{3}}\right]_{0}^{h}={\frac {Bh}{3}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>B</mi> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> </msubsup> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> </mrow> <mi>y</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>B</mi> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <msubsup> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mn>3</mn> </mfrac> </mrow> <mo>]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>B</mi> <mi>h</mi> </mrow> <mn>3</mn> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {B}{h^{2}}}\int _{0}^{h}y^{2}{\rm {d}}y={\frac {B}{h^{2}}}\left[{\frac {y^{3}}{3}}\right]_{0}^{h}={\frac {Bh}{3}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0981a889a9e541d5c45b15af8e1fc4f589d00ae6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:33.007ex; height:6.843ex;" alt="{\displaystyle {\frac {B}{h^{2}}}\int _{0}^{h}y^{2}{\rm {d}}y={\frac {B}{h^{2}}}\left[{\frac {y^{3}}{3}}\right]_{0}^{h}={\frac {Bh}{3}}.}" /></span> </p> </div><div class="clear" style="clear:both;"></div> </div> <div class="mw-heading mw-heading4"><h4 id="Cône_tronqué"><span id="C.C3.B4ne_tronqu.C3.A9"></span>Cône tronqué</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&veaction=edit&section=8" title="Modifier la section : Cône tronqué" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&action=edit&section=8" title="Modifier le code source de la section : Cône tronqué"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Quand on coupe le cône par un plan parallèle à sa base, on obtient deux solides. Celui qui contient le sommet est une réduction du cône original, le second solide est un cône tronqué. Son volume s'exprime, en fonction de ses deux bases B<sub>1</sub> et B<sub>2</sub> et de sa hauteur h (la distance séparant les deux bases) selon la formule : <span style="display: block; margin-left:1.6em;"> <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={\frac {h}{3}}\times (B_{1}+{\sqrt {B_{1}B_{2}}}+B_{2})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>h</mi> <mn>3</mn> </mfrac> </mrow> <mo>×</mo> <mo stretchy="false">(</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </msqrt> </mrow> <mo>+</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V={\frac {h}{3}}\times (B_{1}+{\sqrt {B_{1}B_{2}}}+B_{2})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b192a8affd3e73cd3581843362af52cad890c93" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:30.988ex; height:5.343ex;" alt="{\displaystyle V={\frac {h}{3}}\times (B_{1}+{\sqrt {B_{1}B_{2}}}+B_{2})}" /></span></span> </p> <div class="mw-heading mw-heading3"><h3 id="Cas_du_cône_de_révolution"><span id="Cas_du_c.C3.B4ne_de_r.C3.A9volution"></span>Cas du cône de révolution</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&veaction=edit&section=9" title="Modifier la section : Cas du cône de révolution" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&action=edit&section=9" title="Modifier le code source de la section : Cas du cône de révolution"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fichier:Cone_(geometry).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Cone_%28geometry%29.svg/220px-Cone_%28geometry%29.svg.png" decoding="async" width="220" height="394" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Cone_%28geometry%29.svg/330px-Cone_%28geometry%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/75/Cone_%28geometry%29.svg/440px-Cone_%28geometry%29.svg.png 2x" data-file-width="201" data-file-height="360" /></a><figcaption><a href="/wiki/C%C3%B4ne_de_r%C3%A9volution" title="Cône de révolution">Cône de révolution</a>.</figcaption></figure> <p>Dans le cas particulier du cône de révolution, les formules du volume <b>V</b> et de l'aire <b>A</b> (aire de la surface enfermant le cône: aire latérale + base circulaire) sont </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={\frac {1}{3}}\pi r^{2}\times 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> <mo>×</mo> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V={\frac {1}{3}}\pi r^{2}\times h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/922bda529e123698256efe76a5dc0cb21a7c43b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:14.499ex; height:5.176ex;" alt="{\displaystyle V={\frac {1}{3}}\pi r^{2}\times h}" /></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 A=\pi r(r+a)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mi>r</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo>+</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=\pi r(r+a)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf533ebe607ef500b35e79b550e032e80c9269ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.537ex; height:2.843ex;" alt="{\displaystyle A=\pi r(r+a)\,}" /></span>,</dd></dl> <p>où <i>r</i> est le rayon du cercle de base, <i>h</i> la hauteur du cône et </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={\sqrt {r^{2}+h^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</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 a={\sqrt {r^{2}+h^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41e3b2535eee34887603d7f98b967ee0ff9d6ad7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.989ex; height:3.509ex;" alt="{\displaystyle a={\sqrt {r^{2}+h^{2}}}}" /></span></dd></dl> <p>l'<i><a href="/wiki/Apoth%C3%A8me" title="Apothème">apothème</a></i> du cône. </p> <div class="mw-heading mw-heading4"><h4 id="Aire_latérale"><span id="Aire_lat.C3.A9rale"></span>Aire latérale</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&veaction=edit&section=10" title="Modifier la section : Aire latérale" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&action=edit&section=10" title="Modifier le code source de la section : Aire latérale"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>L'aire latérale <i>A<sub>l</sub></i> (sans la base) vaut </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_{l}=\pi r{\sqrt {r^{2}+h^{2}}}=\pi r^{2}{\sqrt {1+{\frac {h^{2}}{r^{2}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <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> <mo>=</mo> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{l}=\pi r{\sqrt {r^{2}+h^{2}}}=\pi r^{2}{\sqrt {1+{\frac {h^{2}}{r^{2}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fea31051f518e55809daa0d072d5ae5fe408714b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:33.694ex; height:7.509ex;" alt="{\displaystyle A_{l}=\pi r{\sqrt {r^{2}+h^{2}}}=\pi r^{2}{\sqrt {1+{\frac {h^{2}}{r^{2}}}}}}" /></span></dd></dl> <p>or, d'après les relations trigonométriques dans le <a href="/wiki/Triangle_rectangle" title="Triangle rectangle">triangle rectangle</a>, on a </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 1+{\frac {h^{2}}{r^{2}}}={\frac {1}{\sin ^{2}\alpha }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1+{\frac {h^{2}}{r^{2}}}={\frac {1}{\sin ^{2}\alpha }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e0fbce77637c8deac229b5dd9182c23f09154ad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:16.951ex; height:6.176ex;" alt="{\displaystyle 1+{\frac {h^{2}}{r^{2}}}={\frac {1}{\sin ^{2}\alpha }}}" /></span></dd></dl> <p>où α est le demi-angle au sommet. Si <i>A</i><sub>0</sub> est l'aire de la base π⋅<i>r</i> <sup>2</sup>, on a alors </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_{l}={\frac {A_{0}}{\sin \alpha }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{l}={\frac {A_{0}}{\sin \alpha }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ea1f1a75a3d15fdc38b6f72e513c961e169be0b2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:11.131ex; height:5.343ex;" alt="{\displaystyle A_{l}={\frac {A_{0}}{\sin \alpha }}}" /></span></dd></dl> <p>Cette formule sert par exemple à calculer l'aire du <a href="/wiki/Front_de_flamme" title="Front de flamme">front de flamme</a> dans le cas d'une flamme conique, donc la consommation de gaz et la puissance de cette flamme. </p> <div class="clear" style="clear:both;"></div> <div class="mw-heading mw-heading4"><h4 id="Section_du_cône_de_révolution_par_un_plan"><span id="Section_du_c.C3.B4ne_de_r.C3.A9volution_par_un_plan"></span>Section du cône de révolution par un plan</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&veaction=edit&section=11" title="Modifier la section : Section du cône de révolution par un plan" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&action=edit&section=11" title="Modifier le code source de la section : Section du cône de révolution par un plan"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Quand on coupe un solide, cône de révolution, par un plan parallèle à la base, on obtient un cercle. Le rayon <i>r</i><sub>1</sub> de ce cercle s'obtient en fonction du rayon <i>r</i> de la base, de la hauteur <i>h</i> du cône et de la distance <i>h</i><sub>1</sub> entre le plan et le sommet du cône en utilisant le <a href="/wiki/Th%C3%A9or%C3%A8me_de_Thal%C3%A8s" title="Théorème de Thalès">théorème de Thalès</a> : </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 {\frac {r}{h}}={\frac {r_{1}}{h_{1}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>r</mi> <mi>h</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {r}{h}}={\frac {r_{1}}{h_{1}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7fc7ced9621b47e4a623301cf9e6ce2423aa47b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:8.503ex; height:5.176ex;" alt="{\displaystyle {\frac {r}{h}}={\frac {r_{1}}{h_{1}}}}" /></span></dd></dl> <p>Quand on coupe ce même cône par un plan contenant son axe de révolution, on obtient un <a href="/wiki/Triangle_isoc%C3%A8le" title="Triangle isocèle">triangle isocèle</a> de base <i>2r </i>et de hauteur <i>h</i>. </p> <div class="mw-heading mw-heading4"><h4 id="Patron_ou_développement_d'un_cône_de_révolution"><span id="Patron_ou_d.C3.A9veloppement_d.27un_c.C3.B4ne_de_r.C3.A9volution"></span>Patron ou développement d'un cône de révolution</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&veaction=edit&section=12" title="Modifier la section : Patron ou développement d'un cône de révolution" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&action=edit&section=12" title="Modifier le code source de la section : Patron ou développement d'un cône de révolution"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fichier:ConeDev.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/ConeDev.svg/440px-ConeDev.svg.png" decoding="async" width="440" height="292" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/ConeDev.svg/660px-ConeDev.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/ConeDev.svg/880px-ConeDev.svg.png 2x" data-file-width="434" data-file-height="288" /></a><figcaption>Développement du cône de révolution.</figcaption></figure> <p>Pour obtenir le patron d'un cône de révolution de rayon <i>r</i> et de hauteur <i>h</i>, il faut d'abord calculer l'apothème </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={\sqrt {r^{2}+h^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</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 a={\sqrt {r^{2}+h^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41e3b2535eee34887603d7f98b967ee0ff9d6ad7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.989ex; height:3.509ex;" alt="{\displaystyle a={\sqrt {r^{2}+h^{2}}}}" /></span>.</dd></dl> <p>Il suffit alors de tracer un cercle de rayon <i>r</i> et une portion de cercle de rayon <i>a</i> dont l'angle au centre vaut <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 {r}{a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>r</mi> <mi>a</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {r}{a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e15e1499db3205d75ff447b450ed0dab1c02c9ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:2.066ex; height:4.676ex;" alt="{\displaystyle {\frac {r}{a}}}" /></span> de l'angle plein. </p> <div class="clear" style="clear:both;"></div> <div class="mw-heading mw-heading2"><h2 id="Notes_et_références"><span id="Notes_et_r.C3.A9f.C3.A9rences"></span>Notes et références</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&veaction=edit&section=13" title="Modifier la section : Notes et références" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&action=edit&section=13" title="Modifier le code source de la section : Notes et références"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="references-small decimal" style=""> </div> <div class="mw-heading mw-heading2"><h2 id="Voir_aussi">Voir aussi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&veaction=edit&section=14" title="Modifier la section : Voir aussi" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&action=edit&section=14" title="Modifier le code source de la section : Voir aussi"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r194021218">.mw-parser-output .autres-projets>.titre{text-align:center;margin:0.2em 0}.mw-parser-output .autres-projets>ul{margin:0;padding:0}.mw-parser-output .autres-projets>ul>li{list-style:none;margin:0.2em 0;text-indent:0;padding-left:24px;min-height:20px;text-align:left;display:block}.mw-parser-output .autres-projets>ul>li>a{font-style:italic}@media(max-width:720px){.mw-parser-output .autres-projets{float:none}}</style><div class="autres-projets boite-grise boite-a-droite noprint js-interprojets"> <p class="titre">Sur les autres projets Wikimedia :</p> <ul class="noarchive plainlinks"> <li class="commons"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Cone_(geometry)?uselang=fr">Cône (géométrie)</a>, sur <span class="project">Wikimedia Commons</span></li> </ul> </div> <div class="mw-heading mw-heading3"><h3 id="Bibliographie">Bibliographie</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&veaction=edit&section=15" title="Modifier la section : Bibliographie" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&action=edit&section=15" title="Modifier le code source de la section : Bibliographie"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>A. Javary, <i>Traité de géométrie descriptive</i>, 1881 (sur <a href="/wiki/Gallica" title="Gallica">Gallica</a>) : <i> <a rel="nofollow" class="external text" href="http://notices.bnf.fr/AfficherNoticeServlet?idNotice=37251169">Cônes et cylindres, sphère et surfaces du second degré</a></i></li></ul> <div class="mw-heading mw-heading3"><h3 id="Articles_connexes">Articles connexes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&veaction=edit&section=16" title="Modifier la section : Articles connexes" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&action=edit&section=16" title="Modifier le code source de la section : Articles connexes"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Projection_centrale" title="Projection centrale">Projection centrale</a></li> <li><a href="/wiki/St%C3%A9radian" title="Stéradian">Stéradian</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Liens_externes">Liens externes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&veaction=edit&section=17" title="Modifier la section : Liens externes" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=C%C3%B4ne_(g%C3%A9om%C3%A9trie)&action=edit&section=17" title="Modifier le code source de la section : Liens externes"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p class="mw-empty-elt"> </p> <ul><li class="mw-empty-elt"></li> <li class="mw-empty-elt"></li> <li><div class="liste-horizontale"><span class="wd_identifiers">Notices dans des dictionnaires ou encyclopédies généralistes<span class="noprint wikidata-linkback skin-invert"><span class="mw-valign-baseline noviewer" typeof="mw:File"><a href="https://www.wikidata.org/wiki/Q42344?uselang=fr#identifiers" title="Voir et modifier les données sur Wikidata"><img alt="Voir et modifier les données sur Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" data-file-width="600" data-file-height="600" /></a></span></span></span> : <ul><li><a rel="nofollow" class="external text" href="https://denstoredanske.lex.dk//kegle/"><i>Den Store Danske Encyklopædi</i></a></li> <li><a rel="nofollow" class="external text" href="https://encyklopedia.pwn.pl/haslo/;4010089"><i>Internetowa encyklopedia PWN</i></a></li> <li><a rel="nofollow" class="external text" href="https://www.larousse.fr/encyclopedie/divers/c%C3%B4ne/36053"><i>Larousse</i></a></li> <li><a rel="nofollow" class="external text" href="https://snl.no/kjegle_-_matematikk"><i>Store norske leksikon</i></a></li> </ul></div></li> <li><div class="liste-horizontale"><span class="wd_identifiers"><a href="/wiki/Autorit%C3%A9_(sciences_de_l%27information)" title="Autorité (sciences de l'information)">Notices d'autorité</a><span class="noprint wikidata-linkback skin-invert"><span class="mw-valign-baseline noviewer" typeof="mw:File"><a href="https://www.wikidata.org/wiki/Q42344?uselang=fr#identifiers" title="Voir et modifier les données sur Wikidata"><img alt="Voir et modifier les données sur Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" data-file-width="600" data-file-height="600" /></a></span></span></span> : <ul><li><span class="nowrap uid noarchive"><a rel="nofollow" class="external text" href="http://d-nb.info/gnd/4163534-6">GND</a></span></li> <li><span class="nowrap uid noarchive"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph973161">Tchéquie</a></span></li> </ul></div></li></ul> <div class="navbox-container" style="clear:both;"> <table class="navbox collapsible noprint autocollapse" style=""> <tbody><tr><th class="navbox-title" colspan="2" style=""><div style="float:left; width:6em; text-align:left"><div class="noprint plainlinks nowrap tnavbar" style="padding:0; font-size:xx-small; color:var(--color-emphasized, #000000);"><a href="/wiki/Mod%C3%A8le:Palette_Quadriques" title="Modèle:Palette Quadriques"><abbr class="abbr" title="Voir ce modèle.">v</abbr></a> · <a class="external text" href="https://fr.wikipedia.org/w/index.php?title=Mod%C3%A8le:Palette_Quadriques&action=edit"><abbr class="abbr" title="Modifier ce modèle. Merci de prévisualiser avant de sauvegarder.">m</abbr></a></div></div><div style="font-size:110%"><a href="/wiki/Quadrique" title="Quadrique">Quadriques</a></div></th> </tr> <tr> <th class="navbox-group" style="">Quadriques impropres</th> <td class="navbox-list" style=""><div class="liste-horizontale"> <ul><li><a class="mw-selflink selflink">Cône</a> <ul><li><a href="/w/index.php?title=C%C3%B4ne_elliptique&action=edit&redlink=1" class="new" title="Cône elliptique (page inexistante)">Cône elliptique</a> <a href="https://en.wikipedia.org/wiki/Cone#Elliptic_cone" class="extiw" title="en:Cone"><span class="indicateur-langue" title="Article en anglais : « Cone#Elliptic cone »">(en)</span></a> <ul><li><a href="/wiki/C%C3%B4ne_de_r%C3%A9volution" title="Cône de révolution">Cône de révolution</a></li></ul></li></ul></li> <li><a href="/wiki/Cylindre" title="Cylindre">Cylindre</a> <ul><li><a href="/wiki/Cylindre_elliptique" title="Cylindre elliptique">Cylindre elliptique</a> <ul><li><a href="/wiki/Cylindre_de_r%C3%A9volution" title="Cylindre de révolution">Cylindre de révolution</a></li></ul></li> <li><a href="/wiki/Cylindre_hyperbolique" title="Cylindre hyperbolique">Cylindre hyperbolique</a></li> <li><a href="/wiki/Cylindre_parabolique" title="Cylindre parabolique">Cylindre parabolique</a></li></ul></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="">Quadriques propres</th> <td class="navbox-list navbox-even" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Ellipso%C3%AFde" title="Ellipsoïde">Ellipsoïde</a> <ul><li><a href="/wiki/Ellipso%C3%AFde_de_r%C3%A9volution" title="Ellipsoïde de révolution">Ellipsoïde de révolution ou sphéroïde</a> <ul><li><a href="/wiki/Sph%C3%A8re" title="Sphère">Sphère</a></li> <li><a href="/wiki/Sph%C3%A9ro%C3%AFde_de_Maclaurin" title="Sphéroïde de Maclaurin">Sphéroïde de Maclaurin</a></li></ul></li></ul></li> <li><a href="/wiki/Hyperbolo%C3%AFde" title="Hyperboloïde">Hyperboloïde</a> <ul><li><a href="/wiki/Hyperbolo%C3%AFde_%C3%A0_une_nappe" class="mw-redirect" title="Hyperboloïde à une nappe">Hyperboloïde à une nappe</a></li> <li><a href="/wiki/Hyperbolo%C3%AFde_%C3%A0_deux_nappes" class="mw-redirect" title="Hyperboloïde à deux nappes">Hyperboloïde à deux nappes</a></li></ul></li> <li><a href="/wiki/Parabolo%C3%AFde" title="Paraboloïde">Paraboloïde</a> <ul><li><a href="/wiki/Parabolo%C3%AFde_hyperbolique" class="mw-redirect" title="Paraboloïde hyperbolique">Paraboloïde hyperbolique</a></li> <li><a href="/wiki/Parabolo%C3%AFde_elliptique" class="mw-redirect" title="Paraboloïde elliptique">Paraboloïde elliptique</a> <ul><li><a href="/wiki/Parabolo%C3%AFde_circulaire" class="mw-redirect" title="Paraboloïde circulaire">Paraboloïde circulaire</a></li></ul></li></ul></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="">Applications</th> <td class="navbox-list" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Mod%C3%A8le_ellipso%C3%AFdal_de_la_Terre" title="Modèle ellipsoïdal de la Terre">Modèle ellipsoïdal de la Terre</a></li> <li><a href="/wiki/Structure_hyperbolo%C3%AFde" title="Structure hyperboloïde">Structure hyperboloïde</a></li> <li><a href="/wiki/Miroir_(optique)#Formes_de_miroirs" title="Miroir (optique)">Miroirs sphériques, paraboliques, elliptiques et hyperboliques</a> <ul><li><a href="/wiki/Miroir_sph%C3%A9rique" title="Miroir sphérique">Miroir sphérique</a></li> <li><a href="/wiki/Miroir_cylindro-parabolique" title="Miroir cylindro-parabolique">Miroir cylindro-parabolique</a></li></ul></li> <li><a href="/wiki/Lentille_optique#Types_de_lentilles" title="Lentille optique">Lentilles sphériques et cylindriques</a> <ul><li><a href="/wiki/Lentille_asph%C3%A9rique" title="Lentille asphérique">Lentille asphérique</a></li> <li><a href="/wiki/Lentille_%C3%A0_gradient_d%27indice" title="Lentille à gradient d'indice">Lentille à gradient d'indice</a></li></ul></li></ul> </div></td> </tr> </tbody></table> </div> <ul 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