1. Sphere Problem (Solid Mensuration)

Each of the twelve edges of a cube of edge a is tangent to a sphere. Find the volume of that portion of the cube which lies outside the sphere.

2. Re: Sphere Problem (Solid Mensuration)

Attached is the best visual I could steal (ignore the red octahedron) ...

in terms of the sphere radius, $R$, the volume within the cube and outside the sphere ...

$V = R^3\bigg[2\sqrt{2}-\dfrac{\pi}{6}(15\sqrt{2}-16) \bigg]$