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) |

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.

© 1996-9

1999-05-26