Question:
Find the length of an arc of a circle of radius 14 cm which subtends an angle of $36^{\circ}$ at the centre
Solution:
Angle in radians $=$ Angle in degrees $\times \frac{\pi}{180}$
Angle in radians $=$ Angle in degrees $\times \frac{\pi}{180}$
$\theta=\frac{1}{r}$ where $\theta$ is central angle, $l=$ length of arc, $r=$ radius
Therefore angle $=36 \times \frac{\pi}{180}=\frac{\pi}{5}$
Now,
$I=r \times \theta$
$=14 \times \frac{\pi}{5}=14 \times \frac{22}{35}=\frac{44}{5}=8.8$
Therefore the length of the arc is $8.8 \mathrm{~cm}$