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.
- Acceleration
- Accidental Cancellation
- Accumulation Point
- Achilles and the Tortoise Paradox
- Ackermann Function
- Ackermann Number
- Acnode
- Acoptic Polyhedron
- Action
- Acute Angle
- Acute Triangle
- Adams-Bashforth-Moulton Method
- Adams' Method
- Addend
- Addition
- Addition Chain
- Addition-Multiplication Magic Square
- Additive Persistence
- Adem Relations
- Adequate Knot
- Adiabatic Invariant
- Adjacency Matrix
- Adjacency Relation
- Adjacent Fraction
- Adjacent Value