# Annulus

An annulus (meaning little ring in Latin) is a ring-shaped figure between two concentric circles. Below are two examples. Think of an annulus as a circle with a concentric hole in it.

An annulus is something you've probably seen in your everyday life. The face of a CD or the colored rings on an archery target are two examples of objects that form a set of annuli.

## Area of an annulus

The area of an annulus is

A = π(R^{2} - r^{2})

Where R is the radius of the outer circle and r is the radius of the inner circle.

The area, A, of the annulus shown in gray can be found by subtracting the area of the circle, πr^{2}, from the area of the outer circle, πR^{2}. Therefore,

A = πR^{2} - πr^{2} = π(R^{2} - r^{2})

If the diameters of the annulus are given, the area of an annulus is

Where D is the diameter of the outer circle and d is the diameter of the inner circle.

Example:

What is the area of a cross section (the annulus) of a cylindrical concrete water pipe with the following dimensions?

The area of the annulus is:

A = | |

= | |

= | 35π |

Multiplying the area of the cross section by the pipe's length yields the volume, V, of concrete it would take to produce the pipe.

V = 35π × 72 = 2520π