# Annulus Area

Weekly Problem 38 - 2011

Given three concentric circles, shade in the annulus formed by the smaller two. What percentage of the larger circle is now shaded?

Given three concentric circles, shade in the annulus formed by the smaller two. What percentage of the larger circle is now shaded?

## Problem

The three circles in the diagram have the same centre and have radii 3cm, 4cm and 5cm. What percentage of the larger circle is shaded?

Image

## Student Solutions

Ans: 28%

The area of the larger circle is 25$ \pi $ cm $^2$.

The area of the smallest circle is 9$ \pi $ cm $^2$.

The area of the middle circle is 16$ \pi $ cm $ ^2 $.

Therefore the area of the ring is (16$ \pi $ - 9 $ \pi $) cm $ ^2 $ i.e. 7 $ \pi $ cm $^2 $.

Therefore the fraction shaded is $\frac{7 \pi }{25\pi }$

Therefore the percentage shaded is 28%