Question

AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O (see Figure given below). If ∠AOB = 30°, find the area of the shaded region.

Answer 1

(i) Area of segment OAPB = ? 

r = 21 cm, θ = 30°

= \(\frac{1}{12}\) × 3.14 × 49 

= 12.82 sq.cm. 

∴ Area of shaded region 

Area of Sector OAPB – Area of segment OCQD 

= 115.4 – 12.82 

= 102.58 sq.cm.