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.
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\piR3-\tfrac43\pir3\\[3mu] &=\tfrac43\pil(R3-r3r)\\[3mu] &=\tfrac43\pi(R-r)l(R2+Rr+r2r) \end{align}
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 ≈ 4\pir2t,
t\llr
The total surface area of the spherical shell is
4\pir2