document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=858609>Question 858609</A>: <I><SPAN STYLE=\"word-break: break-all;\"> calculus. A cylindrical container is to hold 20&#960; cm3. The bottom is made of a material that costs $0.80 per cm2, and the top is left open (no material needed). The material for the curved side costs $0.32 per cm2.<BR>\n" );
document.write( "Find the height in centimeters of the most economical container.<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 #517291 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=517291\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let h = height, r = radius.<BR>\n" );
document.write( "Let A = surface area<BR>\n" );
document.write( "Let v=volume\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2%2Api%2Ar%5E2%2Ah%2Bpi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"A=2%2Api%2Ar%5E2%2Ah%2Bpi%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=v=h%2Api%2Ar%5E2=20pi ALIGN=MIDDLE  ALT=\"v=h%2Api%2Ar%5E2=20pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Solve this for h:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=20%2F%28r%5E2%29 ALIGN=MIDDLE  ALT=\"h=20%2F%28r%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and substituting into the A equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2%2Api%2Ar%2820%2F%28r%5E2%29%29%2Bpi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"A=2%2Api%2Ar%2820%2F%28r%5E2%29%29%2Bpi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=40%2Api%2Fr%2Bpi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"A=40%2Api%2Fr%2Bpi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,which you will use for applying the costs of the two different parts.\r<BR>\n" );
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document.write( "Now, applying the cost to those two area parts, cost as a function of r, C(r) becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28r%29=%280.32%2940%2Api%2Fr%2B%280.80%29pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"C%28r%29=%280.32%2940%2Api%2Fr%2B%280.80%29pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28C%28r%29=12.8%2Api%2Fr%2B%280.80%29pi%2Ar%5E2%29 ALIGN=MIDDLE  ALT=\"highlight_green%28C%28r%29=12.8%2Api%2Fr%2B%280.80%29pi%2Ar%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "You want to minimize the cost.  Find the derivative of C with regard to r, set equal to zero, and solve this for r.  You then use this to find your value of h.\r<BR>\n" );
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document.write( "You might also want to check your result using a graphing calculator for the cost equation without use of Calculus. </SPAN>\n" );
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