## Zone

The Surface Area of a Spherical Segment. Call the Radius of the Sphere , the upper and lower Radii and , respectively, and the height of the Spherical Segment . The zone is a Surface of Revolution about the z-Axis, so the Surface Area is given by

 (1)

In the -plane, the equation of the zone is simply that of a Circle,
 (2)

so
 (3) (4)

and
 (5)

This result is somewhat surprising since it depends only on the height of the zone, not its vertical position with respect to the Sphere.