## Area Of Annulus

#### Problem

Find the area of the annulus.

#### Solution

Surprisingly it is unnecessary to know the radius of either circle to determine the area of the annulus. Consider the following diagram, where $R$ is the radius of the large circle and $r$ is the area of the small circle.

As a tangent meets a radius at right angles, the triangle is right angled, so $R^2 = r^2 + d^2$.

$$\therefore \pi R^2 = \pi r^2 + \pi d^2$$So the area of the annulus, $\pi R^2 - \pi r^2 = \pi d^2 = 25\pi$.

Problem ID: 341 (26 Jun 2008) Difficulty: 2 Star