# Thread: Sphere Problem (Solid Mensuration)

1. ## Sphere Problem (Solid Mensuration)

Hello, good day to all! Please, I need your help about this problem. Thanks. ☺

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 ...

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

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