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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 .

**^**Weisstein, Eric W. "Spherical Shell".*mathworld.wolfram.com*. Wolfram Research, Inc. Archived from the original on 2 August 2016. Retrieved 7 January 2017.**^**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.