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 z-axis are semicircles.

The volume of the hemisphere is

			(4)
			(5)
			(6)

The weighted mean of over the hemisphere is

(7)

The geometric centroid is then given by

(8)

(Beyer 1987).