Question

If $r=7cm$ and $\theta =60°$, then find the perimeter of the minor sector.

Answer 1

Step $1:$ Convert angle into radians.

Convert the given angle into radians.

$$\begin{gathered} \theta =60° \\ \Rightarrow \theta =60°\times \frac{\mathrm{\pi }}{180°} \\ \Rightarrow \theta =\frac{\mathrm{\pi }}{3} \end{gathered}$$

Step $2:$ Compute the required perimeter.

Assume that, $P$ be the required perimeter.

$P=2r+r\theta$ [Length $\left(l\right)$ of an arc formula is $l=r\theta$]

Substitute the value of $r$ and $\theta$.

$$\begin{gathered} P=2\times 7+7\times \frac{\mathrm{\pi }}{3} \\ \Rightarrow P=14+7.33\left[\because \pi =\frac{22}{7}\right] \end{gathered}$$

Hence, the perimeter of the minor sector is $21.33cm$.