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


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


and the geometric centroid is located at a height


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

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

 I=[1/(10)M(h^2-3Rh+6R^2) 0 0; 0 1/(10)M(h^2-3Rh+6R^2) 0; 0 0 1/5Mh(3R-h)].

The degenerate case of r=h=R gives a hemisphere with circular base, yielding


as expected.

See also

Cone, Hemisphere, Sphere, Spherical Cap, Spherical Sector

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Harris, J. W. and Stocker, H. "Spherical Sector." §4.8.3 in Handbook of Mathematics and Computational Science. New York: Springer-Verlag, pp. 106-107, 1998.Kern, W. F. and Bland, J. R. "Spherical Sector." §37 in Solid Mensuration with Proofs, 2nd ed. New York: Wiley, pp. 103-106, 1948.

Referenced on Wolfram|Alpha

Spherical Cone

Cite this as:

Weisstein, Eric W. "Spherical Cone." From MathWorld--A Wolfram Web Resource.

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