Spherical ring

A ball ring is a solid ball that contains a cylindrical hole. It is bounded on the outside by a symmetrical spherical layer and on the inside by the lateral surface of a straight circular cylinder.

To calculate the spherical ring, enter the radius of the sphere and the radius of the hole a. Then click on the 'Calculate' button

Calculate spherical ring  Input Delete Entries Sphere radius R Cylinder radius r Decimal places 0 1 2 3 4 6 8 10  Results Cylinder volume VC Ring volume VR Cylinder height L Ring surface S

Spherical Ring Formulas

Ring volume (\(\small{V_R}\))

\(\displaystyle V_R=\frac{π·L^3}{6}\)

Cylinder height (\(\small{L}\))

\(\displaystyle L=2·\sqrt{R^2-r^2}\)

Cylinder volume (\(\small{V_C}\))

\(\displaystyle V_{C}=π·L· r^2\)

Ring surface (inside + outside) (\(\small{S}\))

\(\displaystyle S=4· π·(r+R)·\sqrt{R^2-r^2}\) \(\displaystyle \ \ \ =2· π·L ·(r+R)\)

You can find more information about the spherical ring in the tutorial