A spherical sector is a solid of revolution enclosed by two radii from the center of a sphere. The
spherical sector may either be "open" and have a conical hole
(left figure; Beyer 1987), or may be a "closed" spherical
cone (right figure; Harris and Stocker 1998). The volume
of a spherical sector in either case is given by
where
is the vertical distance between where the upper and lower radii intersect
the sphere and
is the sphere's radius.