document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=880814>Question 880814</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I was struggling with this question. Please help me dear tutor . find the height and the radius of a cylinder of volume 150cm^3 which has the least 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 #531719 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=531719\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First find the volume of the cylinder.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=pi%2AR%5E2%2AL=150 ALIGN=MIDDLE  ALT=\"V=pi%2AR%5E2%2AL=150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then first the surface area of the cylinder.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SA=2%2Api%2AR%5E2%2B2%2Api%2AR%2AL ALIGN=MIDDLE  ALT=\"SA=2%2Api%2AR%5E2%2B2%2Api%2AR%2AL\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now substitute from the volume so that the surface area is now only a function of one variable.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=150%2F%28piR%5E2%29 ALIGN=MIDDLE  ALT=\"L=150%2F%28piR%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SA=2%2Api%2AR%5E2%2B2%2Api%2AR%2A%28150%2F%28piR%5E2%29%29 ALIGN=MIDDLE  ALT=\"SA=2%2Api%2AR%5E2%2B2%2Api%2AR%2A%28150%2F%28piR%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SA=2%2Api%2AR%5E2%2B300%2FR ALIGN=MIDDLE  ALT=\"SA=2%2Api%2AR%5E2%2B300%2FR\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To minimize the surface area, take the derivative with respect to R and set it equal to zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%28SA%29%2FdR=4%2Api%2AR-300%2FR%5E2 ALIGN=MIDDLE  ALT=\"d%28SA%29%2FdR=4%2Api%2AR-300%2FR%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Api%2AR-300%2FR%5E2=0%0D%0A%7B%7B%7B4%2Api%2AR=300%2FR%5E2%0D%0A%7B%7B%7BR%5E3=300%2F%284%2Api%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R=%28175%2F%282%2Api%29%29%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"R=%28175%2F%282%2Api%29%29%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then you can work backwards to find L. <BR>\n" );
document.write( " </SPAN>\n" );
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