# Spherical shell

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]}

## Volume

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* ().

## In popular culture

A Dyson sphere encloses a fictitious spherical shell around a star, as first described by author Olaf Stapledon.

## See also

## References

**^**W., Weisstein, Eric. "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; scientific editor, A.A. Abrikosov, Jr. ; translators, A.A. Abrikosov, Jr., J. Vydryg, & D. (2012).*The wonders of physics*(3rd ed.). Singapore: World Scientific. p. 78. ISBN 978-9814374156. Archived from the original on 20 December 2017. Retrieved 7 January 2017.