Answer
The length of the arc in the nearest tenth is $8.4$ inch.
Work Step by Step
To find 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)
Here we have $\theta=80^\circ$ and diameter $d=12$ inch.
- In radians: $\theta=80^\circ\times\frac{\pi}{180^\circ}=\frac{4\pi}{9}$
- The radius of the circle is: $r=\frac{d}{2}=6$ in.
So the length of the arc would be:
$$s=6\times\frac{4\pi}{9}=\frac{8\pi}{3}$$
$$s\approx8.4(in.)$$
