![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() |
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
,
![]() |
![]() |
![]() |
|
![]() |
![]() |
||
![]() |
![]() |
||
![]() |
![]() |
||
![]() |
![]() |
(1) |
![]() |
![]() |
![]() |
(2) |
![]() |
![]() |
![]() |
(3) |
![]() |
![]() |
![]() |
(4) |
![]() |
![]() |
![]() |
(5) |
![]() |
![]() |
![]() |
|
![]() |
![]() |
(6) |
![]() |
(7) |
See also Archimedes' Problem, Frustum, Hemisphere, Sphere, Spherical Cap, Spherical Sector, Surface of Revolution, Zone
References
Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 130, 1987.
![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() |
© 1996-9 Eric W. Weisstein