document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=607004>Question 607004</A>: <I><SPAN STYLE=\"word-break: break-all;\"> an open topcylindrical container has a volume of 100 pie. construct a single-variable object function suited to minimizing the 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 #382519 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=382519\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> an open top cylindrical container has a volume of 100 pie. <BR>\n" );
document.write( "construct a single-variable object function suited to minimizing the surface area?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "x = the radius<BR>\n" );
document.write( "The volume of a cylinder: V = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ax%5E2%2Ah ALIGN=MIDDLE  ALT=\"pi%2Ax%5E2%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ax%5E2%2Ah ALIGN=MIDDLE  ALT=\"pi%2Ax%5E2%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100pi ALIGN=MIDDLE  ALT=\"100pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "divide both side by pi<BR>\n" );
document.write( "x^2*h = 100<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2Fx%5E2 ALIGN=MIDDLE  ALT=\"100%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "The surface area of a open topped cylinder: S.A. = <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=pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "replace h with <BR>\n" );
document.write( "S.A. = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api%2Ax%2A%28100%2Fx%5E2%29 ALIGN=MIDDLE  ALT=\"2%2Api%2Ax%2A%28100%2Fx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ax%5E2 ALIGN=MIDDLE  ALT=\"pi%2Ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cancel x<BR>\n" );
document.write( "S.A. = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api%2A%28100%2Fx%29 ALIGN=MIDDLE  ALT=\"2%2Api%2A%28100%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ax%5E2 ALIGN=MIDDLE  ALT=\"pi%2Ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Graph this equation; y = surface area<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-5%2C+12%2C+-100%2C+400%2C+x-2%2C+%282%2Api%2A%28100%2Fx%29%29%2B%28pi%2Ax%5E2%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Looks like minimum surface area occurs when x=4.64 (radius), height = 4.64 also (100/4.64^2)<BR>\n" );
document.write( "S.A. ~ 200 sq/units </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );