Question:
A sector is cut from a circle of radius 21 cm. The angle of the sector is 150°. Find the length of the arc and the area of the sector.
Solution:
Given:
Radius = 2 cm
Angle of sector $=150^{\circ}$
Now,
Length of the arc $=\frac{2 \pi r \theta}{360}$
$=\frac{2 \times \frac{22}{7} \times 21 \times 150}{360}$
$=55 \mathrm{~cm}$
Area of the sector $=\frac{\pi r^{2} \theta}{360}$
$=\frac{22}{7} \times 21 \times 21 \times \frac{150}{360}$
$=577.5 \mathrm{~cm}$