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.

Related formulas

Variables

VThe volume of the wedge (m3)
αThe dihedral angle of the wedge (radians)
rThe radius of the sphere (m)