A spherical segment is the solid defined by cutting a Sphere with a pair of Parallel Planes. It can be thought of as a Spherical Cap with the top truncated, and so it corresponds to a Spherical Frustum. The surface of the spherical segment (excluding the bases) is called a Zone.
Call the Radius of the Sphere and the height of the segment (the distance from the plane to the top of
Sphere) . Let the Radii of the lower and upper bases be denoted and , respectively.
Call the distance from the center to the start of the segment , and the height from the bottom to the top of the segment
. Call the Radius parallel to the segment , and the height above the center . Then ,
See also Archimedes' Problem, Frustum, Hemisphere, Sphere, Spherical Cap, Spherical Sector, Surface of Revolution, Zone
Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 130, 1987.
© 1996-9 Eric W. Weisstein