document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1061644>Question 1061644</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is an optimization problem.\r<BR>\n" );
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document.write( "The problem states that a cylinder has a volume of 1000 cubic inches; therefore, what dimensions will minimize the surface area? <BR>\n" );
document.write( "The conflict is that the answer I have doesn't match the teacher's answer.<BR>\n" );
document.write( "Here's what I did:\r<BR>\n" );
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document.write( "V = (pi) * (r^2) * h<BR>\n" );
document.write( "1000 = (pi) * (r^2) * h <BR>\n" );
document.write( "1000 / ((pi) * (r^2)) = h\r<BR>\n" );
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document.write( "SA = 2 * ( (pi) * r^2 ) + (2 * (pi) * r * h)<BR>\n" );
document.write( "SA = 2 * ( (pi) * r^2 + (pi) * r * ( 1000 / ((pi) * (r^2)) )<BR>\n" );
document.write( "SA = 2 * ( (pi) * r^2 + 1000/r )<BR>\n" );
document.write( "SA = 2 * (pi) * r^2 + 2000/r\r<BR>\n" );
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document.write( "SA' = 4 * (pi) * r - 2000/(r^2)<BR>\n" );
document.write( "0 = 4 * (pi) * r - 2000/(r^2)<BR>\n" );
document.write( "4 * (pi) * r = 2000/(r^2)<BR>\n" );
document.write( "4 * (pi) * r^3 = 2000<BR>\n" );
document.write( "r^3 = 500 / (pi)<BR>\n" );
document.write( "r = root3 ( 500 / (pi) )\r<BR>\n" );
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document.write( "The problem is that r is supposed to be equal to root3 ( 250 / (p) ).<BR>\n" );
document.write( "Where did I go wrong? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #676407 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=676407\">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( "You did not go wrong.  The radius that gives the minimum total surface area is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sqrt[3]{\frac{500}{\pi}\">.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sqrt[3]{\frac{250}{\pi}\"> cannot possibly be the answer because that radius value yields a surface area that is roughly 28 square inches larger than the surface area of the cylinder with the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sqrt[3]{\frac{500}{\pi}\"> inch radius.\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<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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