document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=967595>Question 967595</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two cylinders are such that the ratio of their base radii is 2 : 1 and the ratio of their heights is 3 : 1. Find the ratio of their respective volumes. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #591427 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=591427\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ratio of heights is 3 to 1.<BR>\n" );
document.write( "ratio of radii of the base is 2 to 1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "ratio of volume is?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "volume = pi * r^2 * h\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let the radius of the smaller cylinder be r.<BR>\n" );
document.write( "then the radius of the larger cylinder is 2r.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let the height of the smaller cylinder be h.<BR>\n" );
document.write( "then the height of the larger cylinder is 3h.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the volume of the smaller cylinder is pi * r^2 * h.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the volume of the larger cylindere is pi * (2r)^2 * (3h).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let v1 = volume of smaller cylinder.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let v2 = volume of larger cylinder.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the ratio of the volume of the smaller cylinder to the volume of the larger cylinder is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "v1 / v2 = (pi * r^2 * h) / (pi * (2 * r)^2 * (3 * h)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "v1 / v2 = (pi * r^2 * h) / (pi * 4 * r^2 * 3 * h)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the pi and the r^2 and the h in the numerator and denominator cancel out and you are left with:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "v1 / v2 = 1 / (4 * 3) which simplfies to:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "v1 / v2 = 1 / 12.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that'a the ratio of the volumes.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "as an example:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let the radius of the smaller cylinder be 5 and the height of the smaller cylinder be 10.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the radius of the larger cylinder is 10 and the height of the larger cylinder is 30.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "v1 = pi * 5^2 * 10 = 250 * pi.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "v2 = pi * 10^2 * 30 = 3000 * pi.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "v1 / v2 = 250 / 3000 - 25 / 300 = 1 / 12.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );