# Find the area of a quadrant of a circle whose circumference is 22 cm.

Answer :

Let r be the radius of the circle. Then,

Circumference $$= \ 22$$ cm

$$\Rightarrow \ 2 \pi r \ = \ 22 \$$
$$\Rightarrow \ 2 \ × \ \frac{22}{7} \ × \ r \ = \ 22$$
$$\Rightarrow \ r \ = \ \frac{7}{2}$$cm

Area of the quadrant of a circle

$$= \ \frac{1}{4} \pi r^2 \ = \ ( \frac{1}{4} \ × \ \frac{22}{7} \ × \ \frac{49}{4})$$

$$= \ \frac{539}{56} \ = \ \frac{77}{8} \ cm^2$$