Question

In the figure given below, 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

(i) Radius of Big circle is the diameter of a small circle. 

∴ Radius of small circle = \(\frac{7}{2}\) = 3.5 cm 

∴ Area of small circle, = πr² 

= \(\frac{22}{7}\) × (3.5)² 

= \(\frac{22}{7}\) × 12.25 

= 3.14 × 12.25 

= 38.47 sq.cm. 

(ii) Area of segment OCB = ? 

Radius, r = 7 cm. θ = 90°

∴ Area of sector OCB – Area of ∆OBC 

= 38.47 – 24.50 = 13.97 sq.cm. 

Similarly, 

Area of sector OAC – Area of ∆OAC 

= 38.47 – 24.50 = 13.97 sq.cm. 

∴ Total area of shaded region : 

= Area of small circle + Area of Minor segment OBC + Area of Minor segment OAC 

= 38.47 + 13.97 + 13.97 

= 66.41 sq.cm.