Question:
Find, in terms of $\pi$, the length of the arc that subtends an angle of $30^{\circ}$ at the centre of a circle of radius $4 \mathrm{~cm}$.
Solution:
The arc length l of a sector of an angle θ in a circle of radius r is given by
$l=\frac{\theta}{360^{\circ}} \times 2 \pi r$
It is given that $r=4 \mathrm{~cm}$ and $\theta=30^{\circ}$. Substituting the value of $r$ and $\theta$ in above equation,
$l=\frac{30^{\circ}}{360^{\circ}} \times 2 \pi \times 4 \mathrm{~cm}$
$=\frac{2 \pi}{3} \mathrm{~cm}$