Spherical shell

spherical shell, right: two halves

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.

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:

$V={\frac {4}{3}}\pi R^{3}-{\frac {4}{3}}\pi r^{3}$

$V={\frac {4}{3}}\pi (R^{3}-r^{3})$

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:

$V\approx 4\pi r^{2}t,$

when t is very small compared to r ($t\ll r$).

In popular culture

A Dyson sphere encloses a fictitious spherical shell around a star, as first described by author Olaf Stapledon.

See also

• Spherical pressure vessel
• Ball
• Solid torus
• Bubble