Spherical sector

In geometry, a spherical sector is a portion of a sphere defined by a conical boundary with apex at the center of the sphere. It can be described as the union of a spherical cap and the cone formed by the center of the sphere and the base of the cap.

If the radius of the sphere is denoted by r and the height of the cap by h, the volume of the spherical sector is

V = \frac {2 \pi r^2 h}{3} \;.

If the radius of the base of the cap is denoted by a, the surface area of the spherical sector is

A = \pi r (2h %2B a) \;.

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