Find the area of a quadrant of a circle whose circumference is 66 cm.

Circumference of circle = 66cm

$$2\pi r = 66$$

$$2 \times \frac{22}{7} \times r = 66$$

$$r = \frac{66 \times 7}{44} = 10.5 \text{ cm}$$

$$\text{Area of quadrant} = \frac{1}{4}\pi r^2$$

$$= \frac{1}{4} \times \frac{22}{7} \times (10.5)^2$$

$$= \frac{1}{4} \times \frac{22}{7} \times 110.25$$

$$= \frac{2425.5}{28} \approx 86.63 \text{ cm}^2$$