Question

In Fig.5, AB and CD are two diameters of a circle with centre O, which are perpendicular to each other. OB is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region. `[\text{Use}pi=22/7]`

Answer 1

AB and CD are the diameters of a circle with centre O.

∴ OA = OB = OC = OD = 7 cm (Radius of the circle)

Area of the shaded region

= Area of the circle with diameter OB + (Area of the semi-circle ACDA − Area of ΔACD)

`=pi(7/2)^2+(1/2xxpixx(7)^2-1/2xxCDxxOA)`

`=22/7xx49/4cm^2+1/2xx22/7xx49cm^2-1/2xx14cmxx7cm`

`=77/2cm^2+77cm^2-49cm^2`

`=66.5cm^2`

Thus, the area of the shaded region is 66.5 cm².