Spherical shell

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.

[1] 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 r is the radius of the inner sphere and R 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 t of the shell:[2] when t is very small compared to r (

The total surface area of the spherical shell is