document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1129803>Question 1129803</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A sphere circumscribes a cube of side 4cm.<BR>\n" );
document.write( "a) What is the radius of the sphere?<BR>\n" );
document.write( "b) Find the ratio of the volume of the sphere and cube </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #746450 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=746450\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If s is the length of the sides of the cube, then  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5Bsphere%5D+=+s%2Asqrt%283%29%2F2+ ALIGN=MIDDLE  ALT=\"+r%5Bsphere%5D+=+s%2Asqrt%283%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <—<<< r is 1/2 the diagonal length of the cube, which is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28s%5E2+%2B+s%5E2+%2B+s%5E2%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28s%5E2+%2B+s%5E2+%2B+s%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5Bsphere%5D+=+2sqrt%283%29+cm ALIGN=MIDDLE  ALT=\"+r%5Bsphere%5D+=+2sqrt%283%29+cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or  about 3.464cm <br>\r<BR>\n" );
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document.write( "b)  Because r can be expressed as a function of s,  the ratios can be found in general (the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E3 ALIGN=MIDDLE  ALT=\"s%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > will cancel), without the need for a specific radius:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V%5Bcube%5D+=+s%5E3+ ALIGN=MIDDLE  ALT=\"+V%5Bcube%5D+=+s%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V%5Bsphere%5D+=+%284%2F3%29%28pi%29%28r%5E3%29++=+%284%2F3%29%28pi%29%28s%2Asqrt%283%29%2F2%29%5E3+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V%5Bsphere%5D%2FV%5Bcube%5D+=+%28%284%2F3%29%28pi%29cross%28s%5E3%29%28sqrt%283%29%2F2%29%5E3%29+%2F+cross%28s%5E3%29+=++%28sqrt%283%29%2F2%29pi+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > or about 2.7207.\r<BR>\n" );
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