/sci/ - Science & Math

A solid is constructed by taking a cube of side lengths S and "cutting out" a sphere of radius R < S, as pictured.

The distance between the center of the sphere and the nearest corner of the cube is L. The angle between the distance between the center of the cube and the center of the sphere and the distance between the center of the sphere and the nearest corner is [math]\phi[/math]. The center of the sphere always intersects with a side of the cube.

What is the volume of the solid?