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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.
Solution
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`
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