Answer
The length of the arc is
(a) $8\pi$ (m)
(b) $\frac{55\pi}{9}$ (m)
Work Step by Step
To find out the length of the arc, we need to employ the formula:
$$s = r\theta$$
$s$: the length of the arc
$r$: radius of the circle
$\theta$: the central angle of the arc (in radians)
(a) $r=10m, \theta=\frac{4\pi}{5}$ radians
The length of the arc would be $$s=10\times\frac{4\pi}{5}$$
$$s=8\pi (m)$$
(b) $r=10m, \theta=110^\circ$
- First, we need to change $\theta$ back to radians:
$$\theta=110^\circ\times\frac{\pi}{180^\circ}=\frac{11\pi}{18}(radians)$$
The length of the arc would be $$s=10\times\frac{11\pi}{18}$$
$$s=\frac{55\pi}{9} (m)$$
