Spherical shell
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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.
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: \begin{align} 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 is the radius of the inner sphere and is the radius of the outer sphere. ==Approximation== An approximation for the volume of a thin spherical shell is the surface area of the inner sphere multiplied by the thickness of the shell: V \approx 4 \pi r^2 t, when is very small compared to ( t \ll r ). The total surface area of the spherical shell is 4 \pi r^2 .
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