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?
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The total volume outside the sphere and in the cube is
{{{4^3 - 4pi*z^3/3}}}
The cube has 8 vertices --> the volume asked for = {{{4^3 - 4pi*z^3/3}}} over 8.
= {{{8 - pi*z^3/6}}}
That volume includes points closer to a vertex AND equidistant from an adjacent vertex.
--> Vol < {{{8 - pi*z^3/6}}}