document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=999834>Question 999834</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cylinder is inscribed in a sphere with radius 6. Find the height h of the cylinder with the maximum possible volume?\r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #617378 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=617378\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "A sphere radius that intersects the edge of the cylinder base is the hypotenuse of a right triangle with legs that are cylinder radius and one-half of the cylinder height.  Given a sphere with radius 6, the radius and height of the cylinder are related thus:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ r^2\ =\ 36\ -\ \left(\frac{h}{2}\right)^2\">\r<BR>\n" );
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document.write( "The volume of the cylinder is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ V\ =\ \pi r^2h\">\r<BR>\n" );
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document.write( "Substituting:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ V(h)\ =\ \pi\left(36\ -\ \left(\frac{h}{2}\right)^2\right)h\">\r<BR>\n" );
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document.write( "Simplifying:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ V(h)\ =\ \pi\left(36h\ -\ \frac{h^3}{4}\right)\">\r<BR>\n" );
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document.write( "Take the first derivative\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ V'(h)\ =\ \pi\left(36\ -\ \frac{3h^2}{4}\right)\">\r<BR>\n" );
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document.write( "Set the first derivative equal to zero and solve for the value of the height that gives the maximum volume.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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