Volume of the ball sector

A spherical sector is a body, which is obtained from a spherical segment and a cone as follows. If the spherical segment is smaller than the hemisphere, then the spherical segment is complemented by a cone whose vertex is at the center of the sphere and the base is the base of the segment. If a segment is larger than a hemisphere, then the specified cone is removed from it. The volume of the ball sector is obtained by adding or subtracting the volumes of the corresponding segment and cone. For the volume of the ball sector, the following formula is obtained:



where R is the radius of the ball, and H is the height of the corresponding ball segment ..