document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=589243>Question 589243</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cube is inscribed in a sphere with diameter 9 inches. What is the volume of the cube? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #374825 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=374825\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The longest distance between vertices in a cube is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > times the side of the cube.<BR>\n" );
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document.write( "REASON:<BR>\n" );
document.write( "The diagonal of one of the faces of a cube is the hypotenuse of a right triangle that has for legs the sides of that face of the cube, of length s. So the length of the diagonal of a face is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28s%5E2%2Bs%5E2%29=sqrt%282s%5E2%29=sqrt%282%29%2As ALIGN=MIDDLE  ALT=\"sqrt%28s%5E2%2Bs%5E2%29=sqrt%282s%5E2%29=sqrt%282%29%2As\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That diagonal and the adjacent edge from another face for a right triangle, with leg lengths <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s ALIGN=MIDDLE  ALT=\"s\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29%2As ALIGN=MIDDLE  ALT=\"sqrt%282%29%2As\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The hypotenuse is the diagonal of the cube, and its length is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28s%5E2%2B%28sqrt%282%29%2As%29%5E2%29=sqrt%28s%5E2%2B2s%5E2%29=sqrt%283s%5E2%29=sqrt%283%29%2As ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If the cube is incribed in a spere of diameter 9 inches, the cube has a 9 inch diagonal and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2As=9 ALIGN=MIDDLE  ALT=\"sqrt%283%29%2As=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=9%2Fsqrt%283%29=3sqrt%283%29 ALIGN=MIDDLE  ALT=\"s=9%2Fsqrt%283%29=3sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The volume of a cube with a side length of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=9%2Fsqrt%283%29=3sqrt%283%29 ALIGN=MIDDLE  ALT=\"s=9%2Fsqrt%283%29=3sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=%283sqrt%283%29%29%5E3=3%5E3%2A%28sqrt%283%29%29%5E3=27%2A3sqrt%283%29=81sqrt%283%29 ALIGN=MIDDLE  ALT=\"V=%283sqrt%283%29%29%5E3=3%5E3%2A%28sqrt%283%29%29%5E3=27%2A3sqrt%283%29=81sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > cubic inches<BR>\n" );
document.write( "(approximately 140.3 cubic inches). </SPAN>\n" );
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