What is "spherical segment"

Spherical \Spher"ic*al\, Spheric \Spher"ic\, a. [L. sphaericus, Gr. ???: cf. F. sph['e]rique.]

1. Having the form of a sphere; like a sphere; globular; orbicular; as, a spherical body.

2. Of or pertaining to a sphere.

3. Of or pertaining to the heavenly orbs, or to the sphere or spheres in which, according to ancient astronomy and astrology, they were set.

   Knaves, thieves, and treachers by spherical predominance.
   --Shak.

   Though the stars were suns, and overburned Their spheric limitations.
   --Mrs. Browning.

   Spherical angle, Spherical co["o]rdinate, Spherical excess, etc. See under Angle, Coordinate, etc.

   Spherical geometry, that branch of geometry which treats of spherical magnitudes; the doctrine of the sphere, especially of the circles described on its surface.

   Spherical harmonic analysis. See under Harmonic, a.

   Spherical lune,portion of the surface of a sphere included between two great semicircles having a common diameter.

   Spherical opening, the magnitude of a solid angle. It is measured by the portion within the solid angle of the surface of any sphere whose center is the angular point.

   Spherical polygon,portion of the surface of a sphere bounded by the arcs of three or more great circles.

   Spherical projection, the projection of the circles of the sphere upon a plane. See Projection.

   Spherical sector. See under Sector.

   Spherical segment, the segment of a sphere. See under Segment.

   Spherical triangle,re on the surface of a sphere, bounded by the arcs of three great circles which intersect each other.

   Spherical trigonometry. See Trigonometry. [1913 Webster] -- Spher"ic*al*ly, adv. -- Spher"ic*al*ness, n.

In geometry, 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 spherical zone.

If the radius of the sphere is called R, the radius of the spherical segment bases r and r, and the height of the segment (the distance from one parallel plane to the other) called h, the volume of the spherical segment is then:

$$V = \frac {\pi h}{6} (3r_1^2 + 3r_2^2 + h^2) \,$$

The area of the spherical zone —which excludes the top and bottom bases— is given by:

A = 2πRh