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Question

Find the area of circular path(shaded region), if in rectangle ABCD and PQRS, AB=PQ=10 cm, BC= 6 cm, BQ=RC=AP=SD= 1 cm. (take π=3.14)

A
31.4 cm2
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B
35.7 cm2
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C
62.8 cm2
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D
82.8 cm2
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Solution

The correct option is B 35.7 cm2
QR=PS= BC-BQ-CR = 6-1-1 = 4 cm

Area of shaded region
= Area of rectangle ABCD
- Area of rectangle PQRS
+ Area of the ring

Area of rectangle = Length×Breadth

Area of rectangle ABCD = AB×AD
= 10×6 = 60 cm2
Area of rectangle PQRS = PQ×QR
= 10×4 = 40 cm2

Area of ring = π(R2r2)
.....(where R = BC2 and r = QR2)
= (3.14)(3222) = 3.14×(9-4)
= 3.14×5 = 15.7

Area of shaded region = 60-40+15.7
= 20 + 15.7
= 35.7 cm2

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