Question

In the following figure, two circles with centres A and B touch each other at the point C. If AC = 8 cm and AB = 3 cm, find the area of the shaded region.

Answer 1

Area of the shaded region can be calculated as shown below,

Area of the shaded region = Area of circle with radius AC − area of circle with radius BC

We have given radius of the outer circle that is 8 cm but we don’t know the radius of the inner circle.

We can calculate the radius of the inner circle as shown below,

`BC=AC-AB`

`∴ BC=8-3` 

`∴ BC=5` 

`∴" Area of the shaded region"=pixx8xx8-pixx5xx5`

`∴" Area of the shaded region"=pixx64-pixx25`

`∴" Area of the shaded region"=pixx39`

Substituting `pi=22/7` we get`

`∴" Area of the shaded region"=22/7xx39`

`∴" Area of the shaded region"=122.57`

Therefore, area of the shaded region is `122.57 cm^2`