Question

What is the arc length of a circle that has a $7\mathrm{cm}$ radius and a central angle that is $40°$? Use $3.14$ for $\pi$ and round your answer to the nearest hundredth.

Answer 1

Find the arc length of the circle:

The arc length of the circle of radius $r$ and angle subtended by arc at centre, $\theta$ in degree, is obtained by the formula $s=\theta \times \frac{\mathrm{\pi }}{180}\times r$.

Given, radius $r=7\mathrm{cm}$ and angle $\mathrm{\theta }=40°$ .

Substitute $r=7\mathrm{cm}$ and angle $\mathrm{\theta }=40°$ in $s=\theta \times \frac{\mathrm{\pi }}{180}\times r$ to obtain the arc length.

$\begin{array}{rcl}s& =& 40°\times \frac{3.14}{180°}\times 7\\ & \Rightarrow & s=4.884\mathrm{cm}\\ \therefore s& \approx & 4.88\mathrm{cm}\end{array}$

Hence, the arc length of the circle is $4.88\text{cm}$.