Spherical shell

From Quire, the open reference·Three-dimensional geometric shape·1 min read

In geometry, a spherical shell (a ball 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#edit

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:

${\displaystyle {\begin{aligned}V&={\tfrac {4}{3\pi R^{3}-{\tfrac {4}{3\pi r^{3}\\[3mu]&={\tfrac {4}{3\pi {\bigl (}R^{3}-r^{3}{\bigr )}\\[3mu$

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]

${\displaystyle V\approx 4\pi r^{2}t,}$

when t is very small compared to r ( ${\displaystyle t\ll r}$ ).

The total surface area of the spherical shell is ${\displaystyle 4\pi r^{2$ .

^ 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.

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