The standard spherical shell at the origin:

Volume and centroid:

A standard Ping-Pong ball, a spherical shell, has a mass of 2.7 grams and an outer radius of 40 millimeters:

It is made of celluloid, which has a density of . Knowing that , find the inner radius of a Ping-Pong ball:

The thickness is the difference between the inner and outer radius:

It was once believed that the universe was a system of concentric celestial spheres. At the center of the universe was Earth, and surrounding it were the spherical shells for the planets and the Sun. There was disagreement about the exact order of the planets and the Sun. Plato and Ptolemy ordered the celestial spheres differently:

Visualize and compare the two philosophers' universes using a set of labeled spherical shells:

A pearl is formed, layer by layer, by a mollusk. The pearl's optical properties come from light reflecting off many translucent layers, as opposed to only an opaque surface layer. The difference that translucent layers make can be seen by creating two sets of nested spherical shells that differ in opacity:

Golf balls have multiple layers, the outer, dimpled shell, and one or more inner layers. Model the outer layer as the RegionDifference between a spherical shell and a collection of balls. Get a distribution for the dimples using the MeshCoordinates of a sphere's mesh:

Discretize the region over an interval to get a "cut-away" view of half of it:

Finally, make a ball for the inner core of the golf ball, offset from the center to get a visual separation of layers:

A balloon can be approximated as a spherical shell. Suppose the balloon is made of 10 units of material. Find out how the thickness depends on the outer radius of the balloon:

Suppose the material is such that under the given conditions it will break if it has thickness less than . Find the largest possible outer radius balloon given that constraint:

Here are some different cases of the solution visualized:

A Ball is the limit of SphericalShell as approaches 0:

A Sphere is the limit of SphericalShell as goes to :

A SphericalShell is the closure of RegionDifference between two concentric Ball regions:

SphericalShell is all points less than from a sphere of radius :

Random spherical shell collections:

Corkscrewing spherical shells:

Nested spherical shells: