Question

How do you find the length of arc subtended by a central angle of $30°$ in a circle of radius $10\mathrm{cm}$?

Answer 1

Find the arc length.

It is given that $\theta =30°$ and $r=10\mathrm{cm}$.

Arc length $s$, subtended by a central angle $\theta$ (in radians) and radius $r$ is given by $s=\frac{\theta }{360°}\left(2\mathrm{\pi r}\right)$ units.

Substitute $\theta =30°$ and $r=10\mathrm{cm}$ in $s=\frac{\theta }{360°}\left(2\mathrm{\pi r}\right)$.

$$\begin{gathered} \Rightarrow s=\frac{30°}{360°}\left(2\pi \times 10\right) \\ \Rightarrow s=\frac{1}{12}\left(20\pi \right) \\ \Rightarrow s=\frac{1}{12}\left(20\times 3.14\right)\left[\because \mathrm{\pi }=3.14\right] \\ \Rightarrow s=\frac{1}{12}\left(62.8\right) \\ \therefore s=5.23 \end{gathered}$$

Hence, arc length is $5.23\mathrm{cm}$.