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

Given,

Circumference = 22 cm

⇒ 2πr = 22

⇒ $2 \times \dfrac{22}{7} \times r$ = 22

⇒ r = $\dfrac{22 \times 7}{22 \times 2} = \dfrac{7}{2}$ = 3.5 cm.

A quadrant of a circle means one of the four equal parts.

∴ The area of a quadrant = $\dfrac{1}{4} \times$ Area of circle

$= \dfrac{1}{4} \times πr^2 \\[1em] = \dfrac{1}{4} \times \dfrac{22}{7} \times (3.5)^2 \\[1em] = \dfrac{1}{4} \times 22 \times 0.5 \times 3.5 \\[1em] = \dfrac{38.5}{4} \\[1em] = \dfrac{385}{40} \\[1em] = \dfrac{77}{8} \text{ cm}^2.$

Hence, area of quadrant = $\dfrac{77}{8}$ cm².