document.write( "Question 972793: A sphere of radius Z is inscribed inside a cube of side length 4. Let v be a vertex of the cube. Let s be the set of points inside the cube and outside the sphere which are closer to v than any other vertex on the cube. What is the volume of s? \n" ); document.write( "

Algebra.Com's Answer #595031 by Alan3354(69443) $\"\"$ $\"About$

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A sphere of radius Z is inscribed inside a cube of side length 4. Let v be a vertex of the cube. Let s be the set of points inside the cube and outside the sphere which are closer to v than any other vertex on the cube. What is the volume of s?
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\n" ); document.write( "The total volume outside the sphere and in the cube is
\n" ); document.write( " $\"4%5E3+-+4pi%2Az%5E3%2F3\"$
\n" ); document.write( "The cube has 8 vertices --> the volume asked for = $\"4%5E3+-+4pi%2Az%5E3%2F3\"$ over 8.
\n" ); document.write( "= $\"8+-+pi%2Az%5E3%2F6\"$
\n" ); document.write( "That volume includes points closer to a vertex AND equidistant from an adjacent vertex.
\n" ); document.write( "--> Vol < $\"8+-+pi%2Az%5E3%2F6\"$ \n" ); document.write( "

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