Question

In Fig., AB and CD are two diameters of a circle perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region

Answer 1

Area of semicircle ACB = \(\frac{πr^2}2\)

= \(\frac{22}7\times\frac{7\times7}2\) = 77 cm²

area of circle with diameter OD = πr² (r = \(\frac{7}2\) = 3.5)

= \(\frac{22}7\times 3.5 \times 3.5\) = 38.5 cm²

Remaining shaded portion in lower semi circle 

= 77 – 38.5 = 38.5 cm² 

Total shaded portion area = 77 + 38.5 = 115.5 cm²