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Spherical Sector


SphericalSector

A spherical sector is a solid of revolution enclosed by two radii from the center of a sphere. The spherical sector may either be "open" and have a conical hole (left figure; Beyer 1987), or may be a "closed" spherical cone (right figure; Harris and Stocker 1998). The volume of a spherical sector in either case is given by

 V=2/3piR^2h,

where h is the vertical distance between where the upper and lower radii intersect the sphere and R is the sphere's radius.


See also

Cylindrical Segment, Sphere, Spherical Cap, Spherical Cone, Spherical Segment, Spherical Wedge, Zone

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References

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 131, 1987.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.Smith, D. E. "Spherical Sector." §542 in Essentials of Plane and Solid Geometry. Boston, MA: Ginn and Co., p. 542, 1923.

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Spherical Sector

Cite this as:

Weisstein, Eric W. "Spherical Sector." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SphericalSector.html

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