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 .