document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=233136>Question 233136</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cylindrical can is to have volume 300 cubic centimetres. Find its height and its<BR>\n" );
document.write( "radius if the total surface area (and hence the total amount of material used) is minimum.<BR>\n" );
document.write( "[The volume is given by V = r2h, and the surface area is S = 2rh + 2r2, where r is the<BR>\n" );
document.write( "radius and h is the height. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #172178 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=172178\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A cylindrical can is to have volume 300 cubic centimetres. Find its height and its<BR>\n" );
document.write( "radius if the total surface area (and hence the total amount of material used) is minimum.<BR>\n" );
document.write( "[The volume is given by V = r2h, and the surface area is S = 2rh + 2r2, where r is the radius and h is the height.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find h in terms of the Volume<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ar%5E2%2Ah ALIGN=MIDDLE  ALT=\"pi%2Ar%5E2%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 300<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300%2F%28pi%2Ar%5E2%29 ALIGN=MIDDLE  ALT=\"300%2F%28pi%2Ar%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Surface area<BR>\n" );
document.write( "S = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api%2Ar%2Ah ALIGN=MIDDLE  ALT=\"2%2Api%2Ar%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api%2Ar%5E2 ALIGN=MIDDLE  ALT=\"2%2Api%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Replace h with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300%2F%28pi%2Ar%5E2%29 ALIGN=MIDDLE  ALT=\"300%2F%28pi%2Ar%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "S = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api%2Ar%2A%28300%2F%28pi%2Ar%5E2%29%29 ALIGN=MIDDLE  ALT=\"2%2Api%2Ar%2A%28300%2F%28pi%2Ar%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api%2Ar%5E2 ALIGN=MIDDLE  ALT=\"2%2Api%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we can cancel pi*r<BR>\n" );
document.write( "S = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28300%2Fr%29 ALIGN=MIDDLE  ALT=\"2%28300%2Fr%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api%2Ar%5E2 ALIGN=MIDDLE  ALT=\"2%2Api%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "S = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28600%2Fr%29 ALIGN=MIDDLE  ALT=\"%28600%2Fr%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api%2Ar%5E2 ALIGN=MIDDLE  ALT=\"2%2Api%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Plot the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api%2Ax%5E2%2B%28600%2Fx%29 ALIGN=MIDDLE  ALT=\"2%2Api%2Ax%5E2%2B%28600%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-4%2C+8%2C+-100%2C+400%2C+2%2Api%2Ax%5E2%2B%28600%2Fx%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-4%2C+8%2C+-100%2C+400%2C+2%2Api%2Ax%5E2%2B%28600%2Fx%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "With the help of a TI83, minimum on this graph: x=3.628, (Min SA ~ 248 sq/cm)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "hence r = 3.628 cm is the radius<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the height<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300%2F%28pi%2A3.628%5E2%29 ALIGN=MIDDLE  ALT=\"300%2F%28pi%2A3.628%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 7.255 cm is the height<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check this by finding the volume with this r and h<BR>\n" );
document.write( "V =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A3.628%5E2%2A7.255 ALIGN=MIDDLE  ALT=\"pi%2A3.628%5E2%2A7.255\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "V = 300.00  <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );