document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=319494>Question 319494</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let A be the ratio of the volume of a sphere to the volume of a cube each of whose face is tangent to the sphere, and let B be the ratio of the surface area of this sphere to the surface area of the cube. Then find the sum A and B. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #228781 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=228781\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let A be the ratio of the volume of a sphere to the volume of a cube each of<BR>\n" );
document.write( " whose face is tangent to the sphere, and let B be the ratio of the surface<BR>\n" );
document.write( " area of this sphere to the surface area of the cube.<BR>\n" );
document.write( " Then find the sum A and B.<BR>\n" );
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document.write( "From the description, the sphere is enclosed in a cube<BR>\n" );
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document.write( "Let r = radius of the sphere <BR>\n" );
document.write( "then<BR>\n" );
document.write( "2r = side of the cube<BR>\n" );
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document.write( "Volume Ratio; sphere/cube <BR>\n" );
document.write( "A  = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%284%2F3%29pi%2Ar%5E3%29%2F%282r%29%5E3 ALIGN=MIDDLE  ALT=\"%28%284%2F3%29pi%2Ar%5E3%29%2F%282r%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%284%2F3%29pi%2Ar%5E3%29%2F%288r%5E3%29 ALIGN=MIDDLE  ALT=\"%28%284%2F3%29pi%2Ar%5E3%29%2F%288r%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cancel r^3<BR>\n" );
document.write( "A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%284%2F3%29pi%29%2F8 ALIGN=MIDDLE  ALT=\"%28%284%2F3%29pi%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%284%2F3%29pi%29%2A%281%2F8%29 ALIGN=MIDDLE  ALT=\"%28%284%2F3%29pi%29%2A%281%2F8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2F3%29pi%29%2A%281%2F2%29 ALIGN=MIDDLE  ALT=\"%28%281%2F3%29pi%29%2A%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F6 ALIGN=MIDDLE  ALT=\"pi%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >; vol ratio<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Surface area ratio; sphere/cube<BR>\n" );
document.write( "B = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2Api%2Ar%5E2%29%2F%286%282r%29%5E2%29 ALIGN=MIDDLE  ALT=\"%284%2Api%2Ar%5E2%29%2F%286%282r%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2Api%2Ar%5E2%29%2F%286%2A4r%5E2%29 ALIGN=MIDDLE  ALT=\"%284%2Api%2Ar%5E2%29%2F%286%2A4r%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2Api%2Ar%5E2%29%2F%2824r%5E2%29 ALIGN=MIDDLE  ALT=\"%284%2Api%2Ar%5E2%29%2F%2824r%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cancel 4, and r^2<BR>\n" );
document.write( "B = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F6 ALIGN=MIDDLE  ALT=\"pi%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "A + B: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F6 ALIGN=MIDDLE  ALT=\"pi%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F6 ALIGN=MIDDLE  ALT=\"pi%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282pi%29%2F6 ALIGN=MIDDLE  ALT=\"%282pi%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F3 ALIGN=MIDDLE  ALT=\"pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );