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Question
In the given figure, O is the centre of the bigger circle, and AC is its diameter. Another circle with AB as diameter is drawn. If AC = 54 cm and BC = 10, find the area of the shaded region.
Solution
We have :
OA = OC = 27 cm
AB = AC - BC
= 54 - 10
= 44
AB is the diameter of the smaller circle.
Thus, we have:
Radius of the smaller circle `="AB"/2 = 44/2 = 22 "cm"`
Area of the smaller circle = πr2
`=22/7xx22xx22`
= 1521.14 cm2
Radius of the larger circle `= "AC"/2 = 54/2 = 27 "cm"`
Area of the larger circle = πr2
`= 22/7xx27xx27`
= 2291.14 cm2
∴ Area of the shaded region = Area of the larger circle -- Area of the smaller circle
= 2291.14 - 1521.14
= 770 cm2
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