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

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

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

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