Spherical wedge (Volume)

Description

A spherical wedge or ungula is a portion of a ball bounded by two plane semidisks and a spherical lune (termed the wedge’s base). The angle between the radii lying within the bounding semidisks is the dihedral angle of the wedge α. If AB is a semidisk that forms a ball when completely revolved about the z-axis, revolving AB only through a given α produces a spherical wedge of the same angle α. (Aspherical wedge is to the sphere of which it is a part as the angle of the wedge is to a perigon.) A spherical wedge of α = π radians (180°) is called a hemisphere, while a spherical wedge of α = 2π radians (360°) constitutes a complete ball. The volume of a spherical wedge can be calculated by the radius of the ball to which the wedge belongs and the dihedral angle of the wedge.