document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=187463>Question 187463</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I'm really struggling on volume and surface area. I have a word problem I have to solve in a worksheet and I'm having trouble. Anyways, the problem is stated exactly as follows: \"Prism A and prism B are similar with a ratio of 2:3. If the volume of prism A is 36 cubic units, what is the volume of prism B? <BR>\n" );
document.write( "If the surface area of prism A is 90 square units, what is the surface area of prism B?\"  Thanks.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #140612 by </B><A HREF=/tutors/aboutme.mpl?userid=scott8148><B>scott8148(6628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=scott8148><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=scott8148><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=140612\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> an example may be helpful\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "suppose we have two similar cubes (yes, ALL cubes are similar)<BR>\n" );
document.write( "one with an edge length of x<BR>\n" );
document.write( "and the other with edge length 2x<BR>\n" );
document.write( "the ratio of the cubes is x:2x or 1:2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the surface area of the smaller cube is 6*x^2 or 6x^2<BR>\n" );
document.write( "the surface area of the larger cube is 6*(2x)^2 or 24x^2<BR>\n" );
document.write( "the ratio of the surface areas is 6x^2:24x^2 or 6:24 or 1:4 or (1:2)^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the volume of the smaller cube is x^3<BR>\n" );
document.write( "the volume of the larger cube is (2x)^3 or 8x^3<BR>\n" );
document.write( "the ratio of the volumes is x^3:8x^3 or 1:8 or (1:2)^3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the ratio of the surface areas is the SQUARE of the proportion ratio<BR>\n" );
document.write( "and the ratio of the volumes is the CUBE of the proportion ratio\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for the prism ___ A:B = 2:3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(A:B)^3 = (2:3)^3 = 8:27\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let x = volume B<BR>\n" );
document.write( "___ 8/27 = 36/x<BR>\n" );
document.write( "___ \"cross\" multiplying ___ 8x = 27*36<BR>\n" );
document.write( "___ dividing by 8 ___ x = 121.5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(A:B)^2 = (2:3)^2 = 4:9\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let y = surface area B<BR>\n" );
document.write( "___ 4/9 = 90/x<BR>\n" );
document.write( "___ \"cross\" multiplying ___ 4x = 810<BR>\n" );
document.write( "___ dividing by 4 ___ x = 202.5 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );