AB and CD are respectively across of two concentric circles of radii 21 cm and 7 cm and centre O (see figure). If \( ∠ \ AOB \ = \ 30º \), find the area of the shaded region.

Let \( A_1 \) and \( A_2 \) be the areas of sectors OAB and OCD respectively. Then,

\( A_1 \) = Area of a sector of angle 30º in a circle of radius 21 cm.

\( = \ \frac{30}{360} \ × \ \frac{22}{7} \ × \ 21 \ × \ 21 \)
[Using \(A \ = \ \frac{ \theta }{360} \ × \ \pi r^2 \)]

\( = \frac{231}{2} \) cm²

\( A_2 \) = Area of a sector of angle 30º in a circle of radius 7 cm

\( = \ \frac{30}{360} \ × \ \frac{22}{7} \ × \ 7 \ × \ 7 \)

\(= \ \frac{77}{6} \) cm²

So, area of the shaded region
\( = \ A_1 \ - \ A_2 \ = \ \frac{231}{2} \ - \ \frac{77}{6} \)

\(= \ \frac{308}{3} \) cm²