document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=484652>Question 484652</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Daughter and I are studying for ACT. Stuck!!!! This question does not belong in this area but we couldn't find anything related to ratios. \r<BR>\n" );
document.write( "\n" );
document.write( "Volume of a cone \r<BR>\n" );
document.write( "\n" );
document.write( "The formula for the volume of a cone is V= 1/3(pi)(r^2)(h) If the radius is doubled and the height is divided by 3, what will be the ratio of the new volume to the original volume? (Is this is a trick? New to Old?)\r<BR>\n" );
document.write( "\n" );
document.write( "The answer is 4:3.\r<BR>\n" );
document.write( "\n" );
document.write( "We are not understanding how to get to this. We can plug numbers into the formula and get to the answer  They show a series of equalities (hopefully the right term) and give no info on how they are reducing the formula. Here is our attempt at typing what is written as an answer.\r<BR>\n" );
document.write( "\n" );
document.write( "V1= new volume r1=new radius h1=h/3 <BR>\n" );
document.write( "V1 = 1/3(pi)(r1^2)h1 = 1/3(pi)(2r^2)(h/3) = 4/9(pi)(r^2)h = 4/3V so the ratio<BR>\n" );
document.write( "V1:V = 4:3\r<BR>\n" );
document.write( "\n" );
document.write( "We absolutely appreciate any help we can get.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #331588 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=331588\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Instead of using all these variables (V1, V, R1, R, h, h1), just use V, V1, r, and h. The volume of the original cone is\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE V = \frac{1}{3}\pi r^2 h\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and the volume of the new cone is\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE V_1 = \frac{1}{3}\pi (2r)^2 \frac{h}{3}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE = \frac{1}{3} \pi 4r^2 \frac{h}{3} = \frac{4}{3} (\frac{1}{3} \pi r^2 h) = \frac{4}{3}V\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hence the ratio of the new volume to the original volume is (4/3)V : V, or 4/3:1   = 4:3. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );