<html>  <head> <title>Forum Cylindre</title> <meta content="text/html; charset=windows-1252" http-equiv="Content-Type"> <meta http-equiv="expires" content="0"> <meta name="Author" content="Alain Larroche"> <meta name="Copyright" content="Epsmag"> <meta name="description" content="Section Cylindre"> <meta name="keywords" content="cylindre, hauteur, longueur, diamtre, lyce, rayon, collge."> <meta name="language" content="french"> <meta http-equiv="pragma" content="no-cache"> <meta name="namo-theme" content="Focus; vert"> <meta name="revisit-after" content="1 week"> <meta name="Robots" content="All"> <style type="text/css">A { 	TEXT-DECORATION: none } </style> <style> .go2 A:hover { 	COLOR: red } .go A:hover { 	BACKGROUND-COLOR: aqua } .go A { 	TEXT-DECORATION: none } </style> </head>  <body bgcolor="#FFFFFF" topmargin="0">  <table border="0" width="100%">   <tr>     <td valign="top" width="125" align="center"><table class="go2" border="0" width="130" cellspacing="0" cellpadding="0">       <tr>         <td width="100%" align="center" valign="bottom"></td>       </tr>       <tr>         <td width="100%" align="center" valign="bottom"><p align="center"><img src="images/epsred.gif" alt="Eps mag" border="0" align="left" WIDTH="130" HEIGHT="30"></td>       </tr>       <tr>         <td width="100%" align="center" valign="bottom"></td>       </tr>       <tr>         <td width="100%" align="center" bgcolor="#FFFFFF" valign="bottom"><img border="0" width="1" height="1"></td>       </tr>     </table>     </td>     <td align="center" width="100%" valign="top"><table border="0" width="100%">       <tr>         <td width="50%" align="center" valign="bottom"></td>       </tr>       <tr>         <td width="50%" align="center" valign="bottom"><table class="go2" border="0" width="100%" cellspacing="0">           <tr>             <td width="16%" align="center"><strong><a href="http://nrm6i/epsmag/forum.htm"><font face="Arial, Helvetica, sans-serif" size="2">Forum</font></a>&nbsp;</strong></td>             <td width="16%" align="center"><font face="Arial, Helvetica, sans-serif" size="2"><a href="http://nrm6i/epsmag/guide.htm"><strong>Math Guide </strong></a></font></td>             <td width="17%" align="center" valign="middle"><font face="Arial, Helvetica, sans-serif" size="2"><a href="http://nrm6i/epsmag/index.htm"><strong>Accueil</strong></a></font></td>             <td width="17%" align="center"><font face="Arial, Helvetica, sans-serif" size="2"><a href="http://nrm6i/epsmag/revue.htm"><strong>Revues</strong></a></font></td>             <td width="17%" align="center"><strong><font face="Arial, Helvetica, sans-serif" size="2"><a href="http://nrm6i/epsmag/pannon.htm">P. 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Il reste une hauteur h de liquide( on connait le         diamtre et la longueur de la citerne). Question: Combien de liquide reste-t-il dans la         citerne?</p>         </font><p>&nbsp;</td>       </tr>       <tr>         <td height="25"></td>       </tr>       <tr>         <td height="50"><img src="http://nrm6i/epsmag/images/Puce1.gif" alt="Puce1.gif (552 octets)" WIDTH="9" HEIGHT="8"><font size="3" color="#FF6600" face="verdana, helvetica, arial"><b> Rponse d'Alain Larroche du 27/01/02  16h 40 :</b></font><p><img src="images/forcyl1.gif" alt="wpeA.jpg (5232 octets)" WIDTH="216" HEIGHT="215"><font size="3" color="#FF6600" face="verdana, helvetica, arial"><b> </b></font></p>         <p><font face="verdana, helvetica, arial" size="3">Le volume de liquide recherch est         gal  L.S si L est la longueur du cylindre et si S correspond  l'aire de la surface         dlimite par l'arc CD et la corde [CD]. Puisque L est connue il suffit de trouver S.         Or, S = S' - S&quot; avec S' reprsentant l'aire du secteur angulaire interceptant l'arc         CD et S&quot; reprsentant l'aire du triangle OCD.</font></p>         <p><font face="verdana, helvetica, arial" size="3">S' = p.R<sup>2</sup>.a/2p = a.R<sup>2</sup>/2         si a est une mesure de l'angle interceptant l'arc CD. </font></p>         <p><font face="verdana, helvetica, arial" size="3">Puisque h = hauteur = AB et OC= Rayon         de la base du cylindre, cos(a/2)=(R-h)/R et a = 2.Arccos[(R-h)/R].</font></p>         <p><font face="verdana, helvetica, arial" size="3">S&quot; = OA.CD/2. Mais CD est connu         puisque OC = R et OA = R-h, CA<sup>2</sup> = OC<sup>2</sup> - OA<sup>2</sup> et CD = 2.CA.</font></p>         <p><font face="verdana, helvetica, arial" size="3">Finalement, V = volume de liquide =         L.(S'-S&quot;).</font></p>         <p><img src="http://nrm6i/epsmag/images/Puce1.gif" alt="Puce1.gif (552 octets)" WIDTH="9" HEIGHT="8"><font size="3" color="#FF6600" face="verdana, helvetica, arial"><b> Rponse de         J-P Houbard du 28/01/02  12h 02 :</b></font></p>         <font face="Arial"><p>En conservant les notations de M.Alain Larroche, il vient en suivant         la mthode prconise&nbsp;:</p>         <p>S' = pi.R<sup>2</sup>.a/2pi = a.R<sup>2</sup>/2 et a = 2Arccos[(R-h)/R].</p>         <p>-&gt; S&#146; = R.Arccos((R-h)/R).</p>         <p>S&#146;&#146;=(|CD|.|OA|) /2=|CA|.|OA|.</p>         <p>S&#146;&#146; = (R-h).(2Rh - h)^(1/2).</p>         <p>Et finalement&nbsp;:</p>         <p>V = L.[ R.Arccos((R-h)/R) - (R-h).(2Rh - h)^(1/2)].</p>         <p>(L&#146;Arccos doit tre exprim en Radian).</p>         <p>&nbsp;</p>         <p>J-P Houbard.</font><ul>           <li><font face="Arial, Helvetica, sans-serif" size="3"><a href="mailto:epsmag77@yahoo.fr">Envoyer</a>             votre rponse.</font><p>&nbsp;</p>             <p>&nbsp;</p>             <p>&nbsp;</p>             <p>&nbsp;</p>             <p><font face="Verdana, Arial, Helvetica" size="2"><br>             </font></p>           </li>         </ul>         </td>       </tr>     </table>     </td>   </tr>   <tr>     <td align="center" width="130" bgcolor="#DFE3C5"></td>     <td align="center" width="240" bgcolor="#DFE3C5" height="8"></td>   </tr> </table> <div align="center"><center>  <table border="0" width="100%">   <tr>     <td align="center" width="120"></td>     <td align="center" width="100%"><font face="Arial, Helvetica, sans-serif" size="2"><em>Copyright      2003 . 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