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spherical shell, right: two halves

In geometry, a spherical shell is a generalization of an annulus to three dimensions. It is the region of a ball between two concentric spheres of differing radii. [1]


The volume of a spherical shell is the difference between the enclosed volume of the outer sphere and the enclosed volume of the inner sphere:

where r is the radius of the inner sphere and R is the radius of the outer sphere.


An approximation for the volume of a thin spherical shell is the surface area of the inner sphere multiplied by the thickness t of the shell: [2]

when t is very small compared to r ().

The total surface area of the spherical shell is .

See also


  1. ^ Weisstein, Eric W. "Spherical Shell". Wolfram Research, Inc. Archived from the original on 2 August 2016. Retrieved 7 January 2017.
  2. ^ Znamenski, Andrey Varlamov; Lev Aslamazov (2012). A.A. Abrikosov Jr. (ed.). The wonders of physics. Translated by A.A. Abrikosov Jr.; J. Vydryg; D. Znamenski (3rd ed.). Singapore: World Scientific. p. 78. ISBN  978-981-4374-15-6.