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Question

# Find the area of the shaded portion in the figure if the diameter of the larger circle is 12 cm.

A

70.71 cm2

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B

69.43 cm2

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C

82.53 cm2

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D

88.53 cm2

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Solution

## The correct option is A 70.71 cm2 We need to find the area of the shaded part here. If we observe the figure, we can make out that the shaded region can be split into 2 semicircles, such that the diameter of the smaller semicircle is equal to the radius of the larger semicircle. The radius of the larger semicircle R =d2 = 6 cm The area of the larger semicircle is =12×π×R2 = 12×227×62 = 56.57 cm2 The radius of the smaller semicircle r = R2 = 3 cm The area of the smaller semicircle = 12×π×32 = 12×227×9 = 14.14 cm2 Therefore,The area of the shaded region = Area of the larger semicircle +Area of the smaller semicircle = 56.57 + 14.14 = 70.71 cm2 The area of the shaded region is 70.71 cm2

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