spherical shell
{{Short description|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.
Volume
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:
:
V &= \tfrac43\pi R^3 - \tfrac43\pi r^3 \\[3mu]
&= \tfrac43\pi \bigl(R^3 - r^3\bigr) \\[3mu]
&= \tfrac43\pi (R-r)\bigl(R^2 + Rr + r^2\bigr)
\end{align}
where {{mvar|r}} is the radius of the inner sphere and {{mvar|R}} is the radius of the outer sphere.
Approximation
See also
References
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