document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1114815>Question 1114815</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two spheres of equal radius are taken out by cutting from a solid cube of side 13cm. What is the maximum volume(in cm^3) of each sphere. </SPAN>\n" );
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document.write( "If sphere is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=inscribed ALIGN=MIDDLE  ALT=\"inscribed\"   DISABLED_style= \"max-width:90%; height:auto;\" > in a cube, the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=diameter ALIGN=MIDDLE  ALT=\"diameter\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the sphere is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=equal ALIGN=MIDDLE  ALT=\"equal\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the length of cube’s <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=edge ALIGN=MIDDLE  ALT=\"edge\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Since you have 2 spheres taken out by cutting from a solid cube  (they are actually inscribed in cube) then the side of the cube equal to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum ALIGN=MIDDLE  ALT=\"sum\"   DISABLED_style= \"max-width:90%; height:auto;\" > of their <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=diameters ALIGN=MIDDLE  ALT=\"diameters\"   DISABLED_style= \"max-width:90%; height:auto;\" > which are equal in length.  \r<BR>\n" );
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document.write( "so, you have \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2d=13cm ALIGN=MIDDLE  ALT=\"2d=13cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=13cm%2F2 ALIGN=MIDDLE  ALT=\"d=13cm%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the length of the each radius is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=d%2F2 ALIGN=MIDDLE  ALT=\"r=d%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=%2813cm%2F2%29%2F2 ALIGN=MIDDLE  ALT=\"r=%2813cm%2F2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=13cm%2F4 ALIGN=MIDDLE  ALT=\"r=13cm%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=3.25cm ALIGN=MIDDLE  ALT=\"r=3.25cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " the maximum volume of each sphere is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=%284%2F3%29pi%2Ar%5E3 ALIGN=MIDDLE  ALT=\"V=%284%2F3%29pi%2Ar%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=%284%2F3%29pi%2A3.25%5E3 ALIGN=MIDDLE  ALT=\"V=%284%2F3%29pi%2A3.25%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=%281.333333333333333%29pi%2A34.328125 ALIGN=MIDDLE  ALT=\"V=%281.333333333333333%29pi%2A34.328125\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=45.77pi ALIGN=MIDDLE  ALT=\"V=45.77pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V ALIGN=MIDDLE  ALT=\"V\"   DISABLED_style= \"max-width:90%; height:auto;\" >&asymp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+143.7178 ALIGN=MIDDLE  ALT=\"+143.7178\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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