document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=839438>Question 839438</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A right cylinder is constructed such that the sum of its radius and twice its height is 18. What should the radius and height be in order to create a cylinder of maximum volume? The radius is represented by x. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #505708 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=505708\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A right cylinder is constructed such that the sum of its radius and twice its height is 18.<BR>\n" );
document.write( "x + 2h = 18<BR>\n" );
document.write( "2h = (18-x)<BR>\n" );
document.write( "h = (9-.5x)<BR>\n" );
document.write( " What should the radius and height be in order to create a cylinder of maximum volume?<BR>\n" );
document.write( " The radius is represented by x.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "V = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ax%5E2%2Ah ALIGN=MIDDLE  ALT=\"pi%2Ax%5E2%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "replace h with (9-.5x)<BR>\n" );
document.write( "V = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ax%5E2%2A%289-.5x%29 ALIGN=MIDDLE  ALT=\"pi%2Ax%5E2%2A%289-.5x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "graphically<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+30%2C+-200%2C+1500%2C+pi%2Ax%5E2%2A%289-.5x%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-6%2C+30%2C+-200%2C+1500%2C+pi%2Ax%5E2%2A%289-.5x%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Max volume at x=12 is the radius<BR>\n" );
document.write( "find the height<BR>\n" );
document.write( "h = 9 - .5(12)<BR>\n" );
document.write( "h = 3 is the height <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );