Find the area of a sector of a circle with radius 7 cm if the angle of the sector is 60°. Class 9

Find the area of a sector of a circle with radius 7 cm if the angle of the sector is 60°. Class 9

Unless stated otherwise, use the approximation $\frac{22}{7}$ for π.

Question 1.

Find the area of a sector of a circle with radius 7 cm if the angle of the sector is 60°. Class 9

Solution:

Radius (r) = 7 cm, Central angle θ = 60°

Area of sector

$\begin{aligned} & =\frac{\theta}{360^{\circ}} \times \pi r^2 \\ & =\frac{60}{360} \times \frac{22}{7} \times(7)^2 \\ & =\frac{1}{6} \times \frac{22}{7} \times 49 \\ & =\frac{154}{6}=25.67\end{aligned}$

∴ Area of the sector = 25.67 cm²

Question 2.

Find the area of a quadrant of a circle whose circumference is 44 cm. Class 9

Solution:

Circumference = 44 cm ...[Given]

∴ 2πr = 44 cm

$\begin{aligned} & 2 \times \frac{22}{7} \times r=44 \\ & \frac{44}{7} \times r=44\end{aligned}$

∴ r = 7 cm

Area of quadrant

$\begin{aligned} & =\frac{1}{4} \times \pi r^2 \\ & =\frac{1}{4} \times \frac{22}{7} \times(7)^2 \\ & =\frac{1}{4} \times \frac{22}{7} \times 49 \\ & =\frac{1}{4} \times 154 \\ & =38.5\end{aligned}$

∴ Area of the quadrant = 38.5 cm²