Q33 of 45 Page 12

In Figure 6, three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these three circles (shaded region). [Use π = 22/7].

(CBSE 2011)

Given: Radius of each circle = 3.5 cm



Join the centers of the three circles. An equilateral triangle of side 7 cm each is formed.


∴ ∠A = ∠B = ∠C = 60° = (π/3) radians


Area of the shaded region = Area of triangle ABC – Area of the three sectors


Area of equilateral triangle = × (Side)2


∴ Area of triangle ABC = × (7)2


= cm2


Area of the sector with central angle A = (1/2) × (∠A/180) × π × r2


= (1/2) × (60/180) × π × 3.5 × 3.5


=


= 77/12


Area of sector with central angle A = Area of sector with central angle B = Area of sector with central angle C


∴ Area of three sectors = 3 × (77/12)


= 77/4


Thus, Area of the shaded region =


= cm2

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