## Annulus

#### Problem

A circle has a unit circle (radius, `r` = 1) removed from its centre to produce an annulus.

If the area remaining is the same as the unit circle removed, find the width of the annulus.

#### Solution

Let the radius of the original circle be, `r`.

If the area remaining is equal to the area removed (a unit circle), the area of the original circle will be twice a unit circle.

π`r`^{2} = 2π `r`^{2} = 2.

Hence, the radius of the original circle, `r` = 2 and so the width of the annulus is 2 1.

Problem ID: 159 (Mar 2004) Difficulty: 2 Star