Spherical shell

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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[edit]


  1. ^ W., Weisstein, Eric. "Spherical Shell". mathworld.wolfram.com. Wolfram Research, Inc. Archived from the original on 2 August 2016. Retrieved 7 January 2017.
  2. ^ 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. {{cite book}}: |first1= has generic name (help)