Spherical segment

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 a zone.

If the radius of the sphere is called r, the radius of the spherical segment bases a and b, 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:

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

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

$A=2\pi rh\,$

See also

• Spherical cap
• Spherical wedge

External links

• Weisstein, Eric W. "Spherical segment". MathWorld.
• Summary of spherical formulas