document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=858725>Question 858725</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is a calculus problem. 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. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #517365 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=517365\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the volume of a cylinder, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=pi%2AR%5E2%2AH=20%2Api ALIGN=MIDDLE  ALT=\"V=pi%2AR%5E2%2AH=20%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5E2%2AH=20 ALIGN=MIDDLE  ALT=\"R%5E2%2AH=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the total cost by calculating the area of the bottom and area of the side wall and multiplying by cost per unit area.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T=pi%2AR%5E2%280.80%29%2B2%2Api%2AR%2AH%2A%280.32%29 ALIGN=MIDDLE  ALT=\"T=pi%2AR%5E2%280.80%29%2B2%2Api%2AR%2AH%2A%280.32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T=0.80%2Api%2AR%5E2%2B0.64%2Api%2AR%2AH ALIGN=MIDDLE  ALT=\"T=0.80%2Api%2AR%5E2%2B0.64%2Api%2AR%2AH\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From the volume equation, you can find a relationship between H and R.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H=20%2FR%5E2 ALIGN=MIDDLE  ALT=\"H=20%2FR%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T=0.80%2Api%2AR%5E2%2B0.64%2Api%2AR%2A%2820%2FR%5E2%29 ALIGN=MIDDLE  ALT=\"T=0.80%2Api%2AR%5E2%2B0.64%2Api%2AR%2A%2820%2FR%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=T=0.80%2Api%2AR%5E2%2B%2812.8%2Api%29%2AR%5E%28-1%29 ALIGN=MIDDLE  ALT=\"T=0.80%2Api%2AR%5E2%2B%2812.8%2Api%29%2AR%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now you have total cost T as a function of one variable.<BR>\n" );
document.write( "Take the derivative and set it to zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dT%2FdR=1.60%2Api%2AR-12.8%2Api%2AR%5E%28-2%29 ALIGN=MIDDLE  ALT=\"dT%2FdR=1.60%2Api%2AR-12.8%2Api%2AR%5E%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.60%2Api%2AR-12.8%2Api%2AR%5E%28-2%29=0 ALIGN=MIDDLE  ALT=\"1.60%2Api%2AR-12.8%2Api%2AR%5E%28-2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.6%2AR=12.8.R%5E2 ALIGN=MIDDLE  ALT=\"1.6%2AR=12.8.R%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=12.8%2F1.6 ALIGN=MIDDLE  ALT=\"R%5E3=12.8%2F1.6\"   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=8 ALIGN=MIDDLE  ALT=\"R%5E3=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<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( "Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H=20%2F%282%5E2%29=5 ALIGN=MIDDLE  ALT=\"H=20%2F%282%5E2%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T=0.80%2Api%2A4%2B0.64%2Api%2A2%2A5 ALIGN=MIDDLE  ALT=\"T=0.80%2Api%2A4%2B0.64%2Api%2A2%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T=10.053%2B20.106 ALIGN=MIDDLE  ALT=\"T=10.053%2B20.106\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T=30.16 ALIGN=MIDDLE  ALT=\"T=30.16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );