document.write( "Question 982137: one sphere is inscribed in a cube while the cube is inscribed in another sphere, what's the ratio of the volumes of the larger sphere to the smaller sphere. \n" ); document.write( "

Algebra.Com's Answer #603060 by mananth(16946) $\"\"$ $\"About$

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\n" ); document.write( "let rsdius of in sphere be r1 with volume v1\r
\n" ); document.write( "\n" ); document.write( "v1= 4/3 pi r1^3\r
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\n" ); document.write( "\n" ); document.write( "radius of outer sphere = $\"sqrt%282%29r1\"$ (by Pythagoras theorem)\r
\n" ); document.write( "\n" ); document.write( "V2= 4/3 pi (sqrt(2))^3*r1\r
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\n" ); document.write( "\n" ); document.write( " $\"V2%2Fv1+=+%28%284%2F3%29+pi+%28sqrt%282%29%29%5E3%2Ar1%29%2F%28%284%2F3%29+pi+r1%5E3%29\"$
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\n" ); document.write( "v2/v1= $\"2sqrt%282%29%2F1\"$ \n" ); document.write( "

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