document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=835432>Question 835432</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two similar cones have a combined volume of 400 in.^3 and the larger cone holds 80 in^3 more than the smaller cone which has a radius of 3 in.  What is the radius of the larger cone? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #503569 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=503569\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let V1 equal volume of smaller cone.<BR>\n" );
document.write( "let V2 equal volume of larger cone.<BR>\n" );
document.write( "V1 + V2 = 400<BR>\n" );
document.write( "V2 = V1 + 80<BR>\n" );
document.write( "replace V2 with V1 + 80 and you get:<BR>\n" );
document.write( "V1 + V1 + 80 = 400<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "2V1 + 80 = 400<BR>\n" );
document.write( "subtract 80 from both sides of the equation to get:<BR>\n" );
document.write( "2V1 = 320<BR>\n" );
document.write( "divide both sides of the equation by 2 to get:<BR>\n" );
document.write( "V1 = 160<BR>\n" );
document.write( "Since V2 = V1 + 80, then:<BR>\n" );
document.write( "V2 = 240<BR>\n" );
document.write( "The ratio of V2 to V1 is equal to 240 / 160 which is equal to 1.5<BR>\n" );
document.write( "The radius of the larger cone will be equal to the cube root of (1.5) * the radius of the smaller cone.<BR>\n" );
document.write( "This makes the radius of the larger cone equal to 3.434142728.\r<BR>\n" );
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document.write( "The solution relies on the fact that the ratio of the individual parts of similar cones is equal to the cube root of the ratio of the volume.\r<BR>\n" );
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document.write( "we can show this in a much simpler example:<BR>\n" );
document.write( "Let's assume V1 = 1/3 * pi * 2^2 * 4 = 1/3 * pi * 4 * 4 = 1/3 * pi * 16<BR>\n" );
document.write( "now let's double the radius and the height.<BR>\n" );
document.write( "That makes V2 = 1/3 * pi * 4^2 * 8 = 1/3 * pi * 16 * 8 = 1/3 * pi * 128<BR>\n" );
document.write( "If we take the ratio of V2 to V1, we will get (1/3 * pi * 128) / (1/3 * pi * 16) which will become 8 because the 1/3 * pi in the numerator and the 1/3 * pi in the denominator will cancel out and you will be left with 128 / 16 which is equal to 8.<BR>\n" );
document.write( "The cube root of 8 is equal to 2.<BR>\n" );
document.write( "That's exactly the ratio of the individual parts.\r<BR>\n" );
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document.write( "the same principle applies in the problem you have above.<BR>\n" );
document.write( "we figured out what the volume of V1 and V2 were.<BR>\n" );
document.write( "we took the ratio of V2 to V1.<BR>\n" );
document.write( "we then took the cube root of that and multiplied the radius of V1 by it to get the radius of V2.\r<BR>\n" );
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