Question

Q.7: In the figure, AB and CD are two diameters of a circle (with centre O) 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

SOLUTION :-

Radius of larger circle, R = 7 cm

Radius of smaller circle, r = 7/2 cm

Height of ΔBCA = OC = 7 cm

Base of ΔBCA = AB = 14 cm

Area of ΔBCA = 1/2 × AB × OC = 1/2 × 7 × 14 = 49 cm²

Area of larger circle = πR2 = 22/7 × 72 = 154 cm²

Area of larger semicircle = 154/2 cm2 = 77 cm²

Area of smaller circle = πr2 = 22/7 × 7/2 × 7/2 = 77/2 cm²

Area of the shaded region = Area of the larger circle – Area of a triangle – Area of larger semicircle + Area of the smaller circle

Area of the shaded region = (154 – 49 – 77 + 77/2) cm²

= 133/2 cm² = 66.5 cm².

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

Answer 2

Step-by-step explanation:

d OD is the diameter of the smaller circle. If O