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.
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:
where is the radius of the inner sphere and 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 of the shell:
when is very small compared to ().
The total surface area of the spherical shell is .