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# 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