document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=940367>Question 940367</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A manufacturer of food-storage containers makes a cylindrical bin with a volume of 1000cm. What dimensions (height and radius) will minimize the material needed to produce each bin, that is minimize the surface area?\r<BR>\n" );
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document.write( "1000 = Pai r^2 h<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #573132 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=573132\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The volume of the can is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=pi%2AR%5E2%2AH=1000 ALIGN=MIDDLE  ALT=\"V=pi%2AR%5E2%2AH=1000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The surface area of the can is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2pi%2AR%5E2%2B2pi%2AR%2AH ALIGN=MIDDLE  ALT=\"A=2pi%2AR%5E2%2B2pi%2AR%2AH\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From the volume equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H=1000%2F%28piR%5E2%29 ALIGN=MIDDLE  ALT=\"H=1000%2F%28piR%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute into the surface area equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2pi%2AR%5E2%2B2pi%2AR%281000%2Fpi%2AR%5E2%29 ALIGN=MIDDLE  ALT=\"A=2pi%2AR%5E2%2B2pi%2AR%281000%2Fpi%2AR%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2pi%2AR%5E2%2B2000%2FR%29 ALIGN=MIDDLE  ALT=\"A=2pi%2AR%5E2%2B2000%2FR%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Take the derivative of area with respect to R and set it equal to zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dA%2FdR=4pi%2AR-2000%2FR%5E2=0 ALIGN=MIDDLE  ALT=\"dA%2FdR=4pi%2AR-2000%2FR%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4pi%2AR=2000%2FR%5E2 ALIGN=MIDDLE  ALT=\"4pi%2AR=2000%2FR%5E2\"   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=500%2Fpi ALIGN=MIDDLE  ALT=\"R%5E3=500%2Fpi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R=%28500%2Fpi%29%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"R=%28500%2Fpi%29%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "SO then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H=1000%2F%28pi%2AR%5E2%29 ALIGN=MIDDLE  ALT=\"H=1000%2F%28pi%2AR%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H=1000%2F%28pi%2A%28500%2Fpi%29%5E%282%2F3%29%29 ALIGN=MIDDLE  ALT=\"H=1000%2F%28pi%2A%28500%2Fpi%29%5E%282%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H=%281000%2F500%5E%282%2F3%29%29%281%2Fpi%5E%281%2F3%29%29 ALIGN=MIDDLE  ALT=\"H=%281000%2F500%5E%282%2F3%29%29%281%2Fpi%5E%281%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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