Spherical Sector

In mathematics, a spherical section or spherical sector refers to a cone-like section from the center of a sphere to its surface.

The following formulas apply to calculate the volume, lateral area and surface area of a spherical section. r denotes the radius of the sphere, a the radius of the base circle and h the height of the sphere segment.

The three sizes a, h and r are dependent on each other. The spherical section is determined by two of these sizes. The third can be calculated from two of the three quantities.

Formulas

In all formulas − is to be taken at ± if the spherical section is less than half the size of the sphere, otherwise + at ±.

Segment radius

Segment height

Sphere radius

Sector volume

surface of the cap

Surface of the cone

Surface of the sector

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