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Question

If AB = 10 cm, what is the area of the shaded portion? It is given that OPA and OQB are quadrants of a circle and AB is a tangent to them. AMR and RNB are two identical semicircles.



A

25(2π4)

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B

25π4

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C

5025π2

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D

None of these

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Solution

The correct option is A

25(2π4)


Area of two small semicircles
=2×π(52)22=25π4cm2



Area of the shaded region=Area of the rectangle
- (Area of the quandrants APQ and BQO)
=(5×10)2π52×14=5025π2
Total area of the shaded region
=5025π2+25π4=25(2π4)


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