document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=798403>Question 798403</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cylinder has a volume of 20 pi inches ^3. The base and top are made of aluminium that costs $4  per sq inch. The sides are made from rolled steel at a cost of $3.2 per sq inch.\r<BR>\n" );
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document.write( "What is the height of the cheapest container?\r<BR>\n" );
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document.write( "So far: V = pi r^2 h  therefore 20pi=pi r^2 h...... therefore h = 20pi/pi r^2<BR>\n" );
document.write( "h=20/r^2 \r<BR>\n" );
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document.write( "Cost= (lid cost)+(base cost)+(side cost)<BR>\n" );
document.write( "Therefore Cost = 4(pi r^2) + 4(pi r^2) + 3.2(2pi r h)<BR>\n" );
document.write( "               = 4(pi r^2) + 4(pi r^2) + 3.2(2pi r)(20/r^2)    subs h\r<BR>\n" );
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document.write( "               = 8(pi r^2) + 128pi/r \r<BR>\n" );
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document.write( "C' therefore = 16pi r - 128pi/r^2\r<BR>\n" );
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document.write( "now I'm stuck, I feel I should multiply top and bottom by r^2 but I cannot see why </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #482183 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=482183\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You seem to be going in the right direction.<BR>\n" );
document.write( "I'll push you the last fraction of an inch.<BR>\n" );
document.write( "For minimum cost, you want C'=0, which  means<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16pi%2Ar%5E2-128pi%2Fr=0 ALIGN=MIDDLE  ALT=\"16pi%2Ar%5E2-128pi%2Fr=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16pir%5E2=128pi%2Fr ALIGN=MIDDLE  ALT=\"16pir%5E2=128pi%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16r%5E3=128 ALIGN=MIDDLE  ALT=\"16r%5E3=128\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> {{r^3=128/16}}} --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E3=8 ALIGN=MIDDLE  ALT=\"r%5E3=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=2 ALIGN=MIDDLE  ALT=\"r=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=20%2Fr%5E2=20%2F2%5E2=20%2F4=highlight%285%29 ALIGN=MIDDLE  ALT=\"h=20%2Fr%5E2=20%2F2%5E2=20%2F4=highlight%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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