## Hemisphere

Half of a Sphere cut by a Plane passing through its Center. A hemisphere of Radius can be given by the usual Spherical Coordinates

 (1) (2) (3)

where and . All Cross-Sections passing through the -axis are Semicircles.

The Volume of the hemisphere is

 (4)

The weighted mean of over the hemisphere is
 (5)

The Centroid is then given by
 (6)

(Beyer 1987).