document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178353>Question 1178353</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cube fits exactly inside a sphere and a smaller sphere fits exactly inside the cube. Find the ratio of the volume of the smaller sphere to the volume of the larger sphere. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #807583 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=807583\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Let r be the radius of the smaller sphere.<br><BR>\n" );
document.write( "Then the edge of the cube is 2r.<br><BR>\n" );
document.write( "The space diagonal of the cube is sqrt(3) times the edge, or 2r*sqrt(3); and it is the diameter of the larger sphere.<br><BR>\n" );
document.write( "So the radius of the larger sphere is r*sqrt(3).<br><BR>\n" );
document.write( "The ratio of the radii of the two spheres is r:r*sqrt(3), or 1:sqrt(3).<br><BR>\n" );
document.write( "The ratio of the volumes is the cube of that ratio.<br><BR>\n" );
document.write( "ANSWER: The ratio of the volume of the smaller sphere to the volume of the larger sphere is 1:3*sqrt(3).<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );