Q31 of 45 Page 12

Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in the given figure. Find the area of the shaded region.

(CBSE 2017)

Area of shaded region = area of semicircle (with radius 4.5 cm) + area of semicircle (with diameter 3 cm) - area of two semicircles(with diameter 3 cm) - area of circle(with radius 4.5 cm)


As,


Area of circle with radius 'r'


Area of semicircle with radius 'r'


Applying formulas in eqn, we get


Area of shaded region = π/2 [ (4.5)2 - (1.5)2 - 2 (1.5)2 - (4.5)2/2] 

Area of shaded region = π/2 [ 20.25 - 2.25 - 5.625]

Area of shaded region = π/2 [ 12.375]



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(CBSE 2011)