document.write( "Question 285377: what is the volume of the region inside a 6 inch cube but outside the sphere? \n" ); document.write( "

Algebra.Com's Answer #206874 by stanbon(75887) $\"\"$ $\"About$

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what is the volume of the region inside a 6 inch cube but outside the sphere?
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\n" ); document.write( "Find the diagonal of the cube:
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\n" ); document.write( "hypotenuse of a face: 6*sqrt(2)
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\n" ); document.write( "diagonal = sqrt(6^2 + (6sqrt(2))^2)
\n" ); document.write( "diagonal = sqrt(36 + 72)
\n" ); document.write( "diagonal = 6sqrt(3)
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\n" ); document.write( "Therefore the radius of the sphere = (1/2)diagonal = 3sqrt(3)
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\n" ); document.write( "So the volume of the sphere = (4/3)(pi)(3sqrt(3))^3
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\n" ); document.write( "The volume of the cube = 6^3 = 216
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\n" ); document.write( "Volume within the sphere but outside the cube
\n" ); document.write( "= (4/3)pi(3sqrt(3)^3 - 216
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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