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]
![](http://upload.wikimedia.org/wikipedia/commons/thumb/0/07/Kugelschale.svg/300px-Kugelschale.svg.png)
Volume
editThe 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.
Approximation
editAn 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
editReferences
edit- ^ 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.