document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=504853>Question 504853</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a cone and a cylinder have the same diameters. How many times greater must the height of the cone be so that the two solids have the same volume? Explain. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #339799 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=339799\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Without loss of generality, suppose the diameter of the cone is 2 (e.g. radius = 1). Then the volume of the sphere is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE V_s = \frac{4}{3}\pi r^3 = \frac{4}{3}\pi\">\r<BR>\n" );
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document.write( "and the volume of the cone is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE V_c = \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi h\">\r<BR>\n" );
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document.write( "Equating the two volumes, we see that h = 4; i.e. the height must be four times the radius, or twice the diameter. </SPAN>\n" );
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