Spherical segment

In geometry, a spherical segment is the solid defined by cutting a sphere or a ball with a pair of parallel planes.

If the radius of the sphere is called R, the radii of the spherical segment bases are a and b, and the height of the segment (the distance from one parallel plane to the other) called h, then the volume of the spherical segment is For the special case of the top plane being tangent to the sphere, we have

and the solid reduces to a spherical cap.

[1] The equation above for volume of the spherical segment can be arranged to Thus, the segment volume equals the sum of three volumes: two right circular cylinders one of radius a and the second of radius b (both of height

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