document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=182723>Question 182723</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You have a cube of gold. Your friend (even though she may not be your friend much longer) has a cube of gold that is twice as long (and wide and high). Your friend's cube weights [  ] as much as yours, and it has [  ] times the surface area. You also have a spherical diamond. Your friend has a spherical diamond of twice the diameter of yours. Your friend's cube weights [  ] as much as yours, and it has [  ] the surface area. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #137196 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=137196\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The the weights of two solid masses of similar material are proportional to their volumes.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The volume of your cube, of edge length <i>s</i> is given by:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math V_{you} = s^3\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since the side length of the larger cube is 2<i>s</i>, the volume of the larger cube must be:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math V_{friend} = (2s)^3 = 8s^3\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So your friend's cube has 8 times the volume and therefore weighs 8 times as much as yours.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The surface area of a cube of edge length <i>s</i> is found by considering that a cube has 6 faces, each of which has an area <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large A_f=s^2\">, therefore the total surface area of your cube is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math A_{you} = 6s^2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And the total surface area of your friend's cube is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math A_{friend} = 6(2s)^2= 24s^2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And your friend's cube has 4 times the surface area as yours.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The problem with the sphere is done in the same fashion.  The formulas for volume and surface area for a sphere are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math V = \frac{4}{3}\pi r^3\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math A_s = 4 \pi r^2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hint:  If your friend's sphere has twice the diameter, it also has twice the radius.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );