document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207300>Question 1207300</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company that manufactures dog food wishes to pack in closed cylindrical tins.<BR>\n" );
document.write( "What should be the dimensions of each tin if it is to have a volume of 128πcm³<BR>\n" );
document.write( "and the minimum possible surface area?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #845093 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=845093\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=pi%2Ar%5E2%2Ah ALIGN=MIDDLE  ALT=\"V=pi%2Ar%5E2%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " surface area:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2pi%2Ar%2Ah%2B2pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"A=2pi%2Ar%2Ah%2B2pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "given\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=128pi%2Acm%5E3 ALIGN=MIDDLE  ALT=\"V=128pi%2Acm%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ar%5E2%2Ah=128pi ALIGN=MIDDLE  ALT=\"pi%2Ar%5E2%2Ah=128pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >...simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2%2Ah=128 ALIGN=MIDDLE  ALT=\"r%5E2%2Ah=128\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=128%2Fr%5E2 ALIGN=MIDDLE  ALT=\"h=128%2Fr%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "substitute in formula for area\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2pi%2Ar%28128%2Fr%5E2%29%2B2pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"A=2pi%2Ar%28128%2Fr%5E2%29%2B2pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2pi%2A%28128%2Fr%29%2B2pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"A=2pi%2A%28128%2Fr%29%2B2pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2pi%2A%28128%2Fr%29%2B2pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"A=2pi%2A%28128%2Fr%29%2B2pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2pi%2Ar%5E2+%2B+%28256pi%29%2Fr ALIGN=MIDDLE  ALT=\"A=2pi%2Ar%5E2+%2B+%28256pi%29%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "to minimize, derivate\r<BR>\n" );
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document.write( "first derivative\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" >′<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r%29=%284pi%2Ar%5E3+-+256pi%29%2Fr%5E2 ALIGN=MIDDLE  ALT=\"%28r%29=%284pi%2Ar%5E3+-+256pi%29%2Fr%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" >′<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r%29=4pi%2Ar-256pi ALIGN=MIDDLE  ALT=\"%28r%29=4pi%2Ar-256pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "second derivative\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" >′'<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r%29=4pi ALIGN=MIDDLE  ALT=\"%28r%29=4pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" >′′<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%29%3E0 ALIGN=MIDDLE  ALT=\"%284%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+4 ALIGN=MIDDLE  ALT=\"r+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is point of minima\r<BR>\n" );
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document.write( "substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=4+ ALIGN=MIDDLE  ALT=\"r=4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=128%2Fr%5E2 ALIGN=MIDDLE  ALT=\"h=128%2Fr%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=128%2F%284%29%5E2 ALIGN=MIDDLE  ALT=\"h=128%2F%284%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=128%2F16 ALIGN=MIDDLE  ALT=\"h=128%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=8 ALIGN=MIDDLE  ALT=\"h=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, minimum surface area the can should have a radius of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4cm+ ALIGN=MIDDLE  ALT=\"4cm+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and height of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8cm ALIGN=MIDDLE  ALT=\"8cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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