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]

spherical shell, right: two halves



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". mathworld.wolfram.com. 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.