document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=133749>Question 133749</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cone-shaped paper cup is to hold 100 cubic cm of water. Find the height and the radius of the cup that can be made from the least amout of paper. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #97895 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=97895\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A cone-shaped paper cup is to hold 100 cubic cm of water. Find the height and the radius of the cup that can be made from the least amount of paper.<BR>\n" );
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document.write( "Use the volume of a cone formula: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >*pi*r^2*h = V; to find h in terms of r.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >*pi*r^2*h = 100<BR>\n" );
document.write( "multiply equation 3 to get rid of the denominator<BR>\n" );
document.write( "pi*r^2*h = 300<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300%2F%28%28pi%2Ar%5E2%29%29 ALIGN=MIDDLE  ALT=\"300%2F%28%28pi%2Ar%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Using the surface area equation: SA = pi*r^2 + (pi*r*L), find L using r and h<BR>\n" );
document.write( "L = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28h%5E2+%2B+r%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28h%5E2+%2B+r%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300%2F%28%28pi%2Ar%5E2%29%29 ALIGN=MIDDLE  ALT=\"300%2F%28%28pi%2Ar%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for h<BR>\n" );
document.write( "L = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28300%2F%28%28pi%2Ar%5E2%29%29%29+%2B+r%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28300%2F%28%28pi%2Ar%5E2%29%29%29+%2B+r%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute above for L in the SA equation<BR>\n" );
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document.write( "SA = (<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;\" >) + (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ar ALIGN=MIDDLE  ALT=\"pi%2Ar\"   DISABLED_style= \"max-width:90%; height:auto;\" >*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28300%2F%28%28pi%2Ar%5E2%29%29%29+%2B+r%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28300%2F%28%28pi%2Ar%5E2%29%29%29+%2B+r%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "Using this equation in my TI83, the graph showed the minimum radius to occur at appox 2.37 cm<BR>\n" );
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document.write( "Find the height using this value:<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300%2F%28%28pi%2A2.37%5E2%29%29 ALIGN=MIDDLE  ALT=\"300%2F%28%28pi%2A2.37%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h = 17 cm<BR>\n" );
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document.write( "Check solution by finding the volume<BR>\n" );
document.write( "V = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > * pi * 2.37^2 * 17<BR>\n" );
document.write( "V = 99.994 ~ 100 cm<BR>\n" );
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document.write( "I was unable to produce the graph here. Hope this helps you.<BR>\n" );
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