2018 · Q98
In the figure given below, the diameter of bigger semicircle is 108 cm. What is the area of the shaded region ?
Elementary MathematicsCircles
- A201 π cm2\text{cm}^2
- B186.3 π cm2\text{cm}^2
- C.5 π cm2\text{cm}^2
- D769.5 π cm2\text{cm}^2
Explanation
The big semicircle (diameter 108, radius 54) has area (pi x 54^2)/2 = 1458 pi. The two unshaded small semicircles (radius 27) total 729 pi, and the small full circle (radius 18) is 324 pi. Shaded area = 1458 pi - 729 pi - 324 pi = 405 pi sq cm. Hence option C.