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<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Cylindre de révolution</span></h1>
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<td colspan="2" class="entete defaut" style="background-color:#E7DCC3;color:black;">Cylindre de révolution
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<tr><td colspan="2" style="text-align:center; line-height: 1.5em;"> <br>Un tronc de cylindre de révolution de <a href="Rayon_(g%C3%A9om%C3%A9trie)" title="Rayon (géométrie)">rayon</a> <span class="texhtml"><i>r</i></span> et de <a href="Hauteur_(g%C3%A9om%C3%A9trie)" title="Hauteur (géométrie)">hauteur</a> <span class="texhtml"><i>h</i></span>.
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<td colspan="2"><hr style="height:2px; background-color:#AAAAAA;"></td></tr>
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<th scope="row">Type</th>
<td><a href="Solide_de_r%C3%A9volution" title="Solide de révolution">Solide de révolution</a></td>
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<th scope="row"><a href="Face_(g%C3%A9om%C3%A9trie)" title="Face (géométrie)">Faces</a>
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<td>2 faces <a href="Cercle" title="Cercle">circulaires</a> et une surface cylindrique
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<td colspan="2"><hr style="height:2px; color:inherit; background-color:#AAAAAA;"></td></tr>
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<th scope="row"><a href="Volume" title="Volume">Volume</a>
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<td><span class="texhtml"><i><a href="Pi" title="Pi">π</a></i> <i>r</i> <sup>2</sup><i> h</i></span>
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<tr>
<th scope="row"><a href="Aire_(g%C3%A9om%C3%A9trie)" title="Aire (géométrie)">Aire</a>
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<td><span class="texhtml">2 <i>π</i> <i>r </i><sup>2</sup> + 2 <i>π</i> <i>r h</i></span>
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<th scope="row">Propriétés
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<td><a href="Construction_%C3%A0_la_r%C3%A8gle_et_au_compas" title="Construction à la règle et au compas">Constructible</a>
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<p>Un <b><a href="Cylindre" title="Cylindre">cylindre</a> circulaire droit</b> ou <b>cylindre de révolution</b> est la <a href="Surface_de_r%C3%A9volution" title="Surface de révolution">surface engendrée par la révolution</a>, autour d'un <a href="Axe_de_rotation" title="Axe de rotation">axe</a> fixe, d'une <a href="Droite_(math%C3%A9matiques)" title="Droite (mathématiques)">droite</a> <a href="Parall%C3%A9lisme_(g%C3%A9om%C3%A9trie)" title="Parallélisme (géométrie)">parallèle</a> à ce dernier. On notera <span class="texhtml mvar" style="font-style:italic;">r</span> le rayon et <span class="texhtml mvar" style="font-style:italic;">h</span> la hauteur d'un tronc de cylindre.
</p>
<div class="mw-heading mw-heading2"><h2 id="Équation_cartésienne"><span id=".C3.89quation_cart.C3.A9sienne"></span><a href="%C3%89quation_cart%C3%A9sienne" title="Équation cartésienne">Équation cartésienne</a></h2></div>
<p>Dans l'espace rapporté au <a href="Rep%C3%A8re_orthonormal" class="mw-redirect" title="Repère orthonormal">repère orthonormal</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (O,{\vec {i}},{\vec {j}},{\vec {k}})}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mo stretchy="false">(</mo>
<mi>O</mi>
<mo>,</mo>
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<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>i</mi>
<mo stretchy="false">→<!-- → --></mo>
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</mrow>
<mo>,</mo>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>j</mi>
<mo stretchy="false">→<!-- → --></mo>
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</mrow>
<mo>,</mo>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>k</mi>
<mo stretchy="false">→<!-- → --></mo>
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</mrow>
<mo stretchy="false">)</mo>
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<annotation encoding="application/x-tex">{\displaystyle (O,{\vec {i}},{\vec {j}},{\vec {k}})}</annotation>
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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/5e34832629ddae6c35ccec8c457b2854fb287dcb.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.084ex; height:3.343ex;" alt="{\displaystyle (O,{\vec {i}},{\vec {j}},{\vec {k}})}" loading="lazy"></span>, le cylindre de révolution d'axe <span class="texhtml"><i>Oz</i></span> et de rayon <span class="texhtml"><i>r</i></span> a pour <a href="%C3%89quation" title="Équation">équation</a> :
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><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}=r^{2}.}">
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<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msup>
<mi>x</mi>
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<mn>2</mn>
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<mo>+</mo>
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<mi>y</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
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</msup>
<mo>=</mo>
<msup>
<mi>r</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
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</msup>
<mo>.</mo>
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</mrow>
<annotation encoding="application/x-tex">{\displaystyle x^{2}+y^{2}=r^{2}.}</annotation>
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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f5ed9d9763124224deaef61d1c3e93b8de55d911.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.287ex; height:3.009ex;" alt="{\displaystyle x^{2}+y^{2}=r^{2}.}" loading="lazy"></span></dd></dl>
<div class="mw-heading mw-heading2"><h2 id="Équation_cylindrique"><span id=".C3.89quation_cylindrique"></span>Équation cylindrique</h2></div>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \,\rho =r.}">
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<mi>ρ<!-- ρ --></mi>
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<annotation encoding="application/x-tex">{\displaystyle \,\rho =r.}</annotation>
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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/03c9479c4de34674a39e308fff5bcea73a8c2268.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.383ex; height:2.176ex;" alt="{\displaystyle \,\rho =r.}" loading="lazy"></span></dd></dl>
<div class="mw-heading mw-heading2"><h2 id="Caractéristiques"><span id="Caract.C3.A9ristiques"></span>Caractéristiques</h2></div>
<div class="mw-heading mw-heading3"><h3 id="Périmètre_d'une_base"><span id="P.C3.A9rim.C3.A8tre_d.27une_base"></span>Périmètre d'une base</h3></div>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2\pi r.}">
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<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mn>2</mn>
<mi>π<!-- π --></mi>
<mi>r</mi>
<mo>.</mo>
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<annotation encoding="application/x-tex">{\displaystyle 2\pi r.}</annotation>
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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c3b803d1afdc1087c903a66aa5febe6624928c5f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.19ex; height:2.176ex;" alt="{\displaystyle 2\pi r.}" loading="lazy"></span></dd></dl>
<div class="mw-heading mw-heading3"><h3 id="Aire_d'une_base"><span id="Aire_d.27une_base"></span>Aire d'une base</h3></div>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi r^{2}.}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>π<!-- π --></mi>
<msup>
<mi>r</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
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</msup>
<mo>.</mo>
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<annotation encoding="application/x-tex">{\displaystyle \pi r^{2}.}</annotation>
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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/43202502a74e533c615c61829a059b87103820e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.082ex; height:2.676ex;" alt="{\displaystyle \pi r^{2}.}" loading="lazy"></span></dd></dl>
<div class="mw-heading mw-heading3"><h3 id="Aire_latérale"><span id="Aire_lat.C3.A9rale"></span>Aire latérale</h3></div>
<p>C'est le produit du périmètre de la base par la hauteur :
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2\pi rh.}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mn>2</mn>
<mi>π<!-- π --></mi>
<mi>r</mi>
<mi>h</mi>
<mo>.</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle 2\pi rh.}</annotation>
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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f69a8d7e53b548ebd3485dd185f0296dfdb0de7c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.529ex; height:2.176ex;" alt="{\displaystyle 2\pi rh.}" loading="lazy"></span></dd></dl>
<div class="mw-heading mw-heading3"><h3 id="Volume">Volume</h3></div>
<p>C'est le produit de l'aire de la base par la hauteur :
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi r^{2}h.}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>π<!-- π --></mi>
<msup>
<mi>r</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
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</msup>
<mi>h</mi>
<mo>.</mo>
</mstyle>
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<annotation encoding="application/x-tex">{\displaystyle \pi r^{2}h.}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4c49239dad3b3a5e32d27bf5cc156c8e9f2a6283.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.421ex; height:2.676ex;" alt="{\displaystyle \pi r^{2}h.}" loading="lazy"></span></dd></dl>
<div class="mw-heading mw-heading2"><h2 id="Voir_aussi">Voir aussi</h2></div>
<ul><li><a rel="nofollow" class="external text" href="https://mathcurve.com/surfaces/cylindrederevolution/cylindrederevolution.shtml">Cylindre de révolution</a> sur MathCurve.<div class="navbox-container" style="clear:both;"></div></li></ul>
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