document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=962508>Question 962508</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello friends. I have a problem here that I am hoping someone can help me with . A right cylinder has a volume of 2pi cubic inches . Find the can dimensions that require the least amount of aluminum to be used in the can construction?  Thank you in advance !!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #588090 by </B><A HREF=/tutors/aboutme.mpl?userid=hkwu><B>hkwu(60)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=hkwu><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=hkwu><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=588090\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The volume is described by<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ar%5E2%2Ah=2pi ALIGN=MIDDLE  ALT=\"pi%2Ar%5E2%2Ah=2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=%282pi%29%2F%28pi%2Ar%5E2%29=2%2Fr%5E2 ALIGN=MIDDLE  ALT=\"h=%282pi%29%2F%28pi%2Ar%5E2%29=2%2Fr%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The surface area is described by<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SA=2pi%2Ah%2B2%2Api%2Ar ALIGN=MIDDLE  ALT=\"SA=2pi%2Ah%2B2%2Api%2Ar\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SA=2pi%2A%282%2Fr%5E2%29%2B2%2Api%2Ar ALIGN=MIDDLE  ALT=\"SA=2pi%2A%282%2Fr%5E2%29%2B2%2Api%2Ar\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SA=%284pi%29%2Fr%2B2%2Api%2Ar%5E2 ALIGN=MIDDLE  ALT=\"SA=%284pi%29%2Fr%2B2%2Api%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Taking the derivative, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F%28dr%29%2ASA=-4pi%2Fr%5E2%2B4pi%2Ar ALIGN=MIDDLE  ALT=\"d%2F%28dr%29%2ASA=-4pi%2Fr%5E2%2B4pi%2Ar\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F%28dr%29%2ASA=%28-4pi%2B4pi%2Ar%5E3%29%2Fr%5E2 ALIGN=MIDDLE  ALT=\"d%2F%28dr%29%2ASA=%28-4pi%2B4pi%2Ar%5E3%29%2Fr%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which is equal to zero when<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4pi%2B4pi%2Ar%5E3=0 ALIGN=MIDDLE  ALT=\"-4pi%2B4pi%2Ar%5E3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2Br%5E3=0 ALIGN=MIDDLE  ALT=\"-1%2Br%5E3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E3=1 ALIGN=MIDDLE  ALT=\"r%5E3=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=1 ALIGN=MIDDLE  ALT=\"r=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If you do the first derivative test, you'll find that this is indeed a minimum value. Thus<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=2%2F1%5E2=2 ALIGN=MIDDLE  ALT=\"h=2%2F1%5E2=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so the optimal dimensions are 1in radius by 2in height. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );