Spherical Cone

The surface of revolution obtained by cutting a conical "wedge" with vertex at the center of a sphere out of the sphere. It is therefore a cone plus a spherical cap, and is a degenerate case of a spherical sector. The volume of the spherical cone is

(1)

(Kern and Bland 1948, p. 104). The surface area of a closed spherical sector is

(2)

and the geometric centroid is located at a height

(3)

above the sphere's center (Harris and Stocker 1998).

The inertia tensor of a uniform spherical cone of mass is given by

(4)

The degenerate case of gives a hemisphere with circular base, yielding

			(5)
			(6)

as expected.