Spherical Segment
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 toptruncated, 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 ofSphere) 
. 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 
,
 |  |  | |
|  | ||
|  | ||
|  | ||
|  | (1) |
Using
 | |  | (2) |
 | |  | (3) |
gives
 | |  | (4) |
 | |  | (5) |
so
| |  | |
|  | (6) |
The surface area of the Zone (which excludes the top and bottom bases) is given by
 | (7) |
References
Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 130, 1987.
- Stella Octangula Number
- Stellated Polyhedron
- Stellated Tetrahedron
- Stellated Truncated Hexahedron
- Stellation
- Stem-and-Leaf Diagram
- Step
- Step Function
- Step Polynomial
- Steradian
- Stereogram
- Stereographic Projection
- Stereology
- Stern-Brocot Tree
- Stevedore's Knot
- Stewart's Theorem
- Stickelberger Relation
- Stick Number
- Stiefel Manifold
- Stiefel-Whitney Class
- Stiefel-Whitney Number
- Stieltjes Constants
- Stieltjes Integral
- Stieltjes' Theorem
- Stieltjes-Wigert Polynomial