Zone
The Surface Area of a Spherical Segment. Call the Radius of the Sphere 
, the upper and lowerRadii 
and 
, respectively, and the height of the Spherical Segment 
. The zone is aSurface of Revolution about the z-Axis, so the Surface Area is given by
 | (1) |
-plane, the equation of the zone is simply that of a Circle, | (2) |
 |  |  | (3) |
 | |  | (4) |
and
 | |  | |
|  | ||
|  | (5) |
This result is somewhat surprising since it depends only on the height of the zone,not its vertical position with respect to the Sphere.See also Sphere, Spherical Cap, Spherical Segment, Zonohedron
References
Beyer, W. H. (Ed.). CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 130, 1987.
- Golden Triangle
- Goldschmidt Solution
- Golomb Constant
- Golomb-Dickman Constant
- Golomb Ruler
- Golygon
- Gomory's Theorem
- Gompertz Constant
- Gompertz Curve
- Gonal Number
- Goodman's Formula
- Good Path
- Good Prime
- Goodstein Sequence
- Goodstein's Theorem
- Googol
- Googolplex
- Gordon Function
- Gorenstein Ring
- Gosper Island
- Gosper's Algorithm
- Gosper's Method
- Graceful Graph
- Graded Algebra
- Gradian