Spherical shell
Three-dimensional geometric shape
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.
01Volume
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:
![{\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]&={\tfrac {4}{3}}\pi (R-r){\bigl (}R^{2}+Rr+r^{2}{\bigr )}\end{aligned}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/eb99f83c65f0782b2fc723b1d5e22b23f09b85b8)
where r is the radius of the inner sphere and R is the radius of the outer sphere.
02Approximation
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:
when t is very small compared to r (
The total surface area of the spherical shell is 
Sources and credits
This article is adapted from the Wikipedia article “Spherical shell”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.
Images, from Wikimedia Commons:
- Kugelschale.svg by Ag2gaeh, CC BY-SA 4.0
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