document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1129435>Question 1129435</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Alya wants to use a piece of rectangular aluminum to build an open cylinder on both ends. If the perimeter of the aluminum piece is 32 cm, find the length and width, in cm, of the aluminum piece so that the volume of the cylinder built is maximum  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #746079 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=746079\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Alya wants to use a piece of rectangular aluminum to build an open cylinder on both ends.<BR>\n" );
document.write( " If the perimeter of the aluminum piece is 32 cm, find the length and width, in cm, of the aluminum piece so that the volume of the cylinder built is maximum <BR>\n" );
document.write( ":<BR>\n" );
document.write( "let x = the width of the aluminum piece<BR>\n" );
document.write( "let L = the length<BR>\n" );
document.write( "the perimeter<BR>\n" );
document.write( "2L + 2x = 32<BR>\n" );
document.write( "simplify, divide by 2<BR>\n" );
document.write( "L + x = 16<BR>\n" );
document.write( "L = (-x+16)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The circumference is the width = x, the height is the Length = (-x+16)<BR>\n" );
document.write( "Find r using the circumference<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api%2Ar ALIGN=MIDDLE  ALT=\"2%2Api%2Ar\"   DISABLED_style= \"max-width:90%; height:auto;\" > = x<BR>\n" );
document.write( "r = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28%282%2Api%29%29 ALIGN=MIDDLE  ALT=\"x%2F%28%282%2Api%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "The volume equation<BR>\n" );
document.write( "V = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ar%5E2%2Ah ALIGN=MIDDLE  ALT=\"pi%2Ar%5E2%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "replace r with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28%282%2Api%29%29 ALIGN=MIDDLE  ALT=\"x%2F%28%282%2Api%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, replace h with (-x+16)<BR>\n" );
document.write( "V = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A%28x%2F%282%2Api%29%29%5E2%2A%28-x%2B16%29 ALIGN=MIDDLE  ALT=\"pi%2A%28x%2F%282%2Api%29%29%5E2%2A%28-x%2B16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "V = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A%28x%5E2%2F%284%2Api%5E2%29%29%2A%28-x%2B16%29 ALIGN=MIDDLE  ALT=\"pi%2A%28x%5E2%2F%284%2Api%5E2%29%29%2A%28-x%2B16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cancel pi<BR>\n" );
document.write( "V = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2F%284%2Api%29%29%2A%28-x%2B16%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2F%284%2Api%29%29%2A%28-x%2B16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "plot this equation, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+20%2C+-10%2C+60%2C+%28x%5E2%2F%284%2Api%29%29%2A%28-x%2B16%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Max volume occurs when x = 10.67 cm<BR>\n" );
document.write( "Find the height (length)<BR>\n" );
document.write( "16 - 10.67 = 5.33 cm<BR>\n" );
document.write( ":<BR>\n" );
document.write( "the aluminum sheet should be 10.67 by 5.33 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );