document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1125333>Question 1125333</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular solid (with a square base) has a surface area of 121.5 square centimeters. Find the dimensions that will result in a solid with maximum volume.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #741661 by </B><A HREF=/tutors/aboutme.mpl?userid=Aaleia><B>Aaleia(1)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Aaleia><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=741661\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Original Poster here and I got it already so no worries! Heres the work.\r<BR>\n" );
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document.write( "Let x = the side of the square base and y = height<BR>\n" );
document.write( "Let V = volume = x2y<BR>\n" );
document.write( "The surface area = 2x2 + 4xy = 121.5<BR>\n" );
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document.write( "Solve surface area equation for y = (121.5 - 2x2)/4x and sub this into the volume equation<BR>\n" );
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document.write( "V = x2(121.5 - 2x2)/4x = x(121.5 - 2x2)/4<BR>\n" );
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document.write( "derivative of V with respect to x = (x/4)(-2x) + (1/4)(121.5 - 2x2) = 0 at the maximum<BR>\n" );
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document.write( "(1/4)(-4x2 + 121.5 - 2x2) = 0<BR>\n" );
document.write( "6x2 = 121.5<BR>\n" );
document.write( "x2 = 20.25<BR>\n" );
document.write( "x = 4.5<BR>\n" );
document.write( "y = (121.5 - 40.5)/(4 * 4.5) =81/18 = 4.5 -> max volume with side 4.5<BR>\n" );
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