document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1088456>Question 1088456</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the radius and height of a cylinder is 20 cm. The dimensions are whole numbers.<BR>\n" );
document.write( "What is the largest possible volume of this cylinder?<BR>\n" );
document.write( "Answer in terms of &#960;. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #702748 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=702748\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> radius is x<BR>\n" );
document.write( "height is 20-x<BR>\n" );
document.write( "volume is pi*r^2*h=pi*x^2(20-x)=pi(20x^2-x^3)<BR>\n" );
document.write( "maximize this<BR>\n" );
document.write( "take the derivative and get -3x^2+40x, and set it equal to 0<BR>\n" );
document.write( "3x^2-40x=0<BR>\n" );
document.write( "factor out an x and divide by 3, moving the constant, x=40/3<BR>\n" );
document.write( "whole number dimension for radius is 13 largest whole number.<BR>\n" );
document.write( "height is 7 cm<BR>\n" );
document.write( "volume is pi (169)*7=1183 pi  ANSWER<BR>\n" );
document.write( "check with height of 8 and volume of 12=1152 pi<BR>\n" );
document.write( "check with height of 6 and volume of 14=1176 pi<BR>\n" );
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