#### Answer

$\approx$ 30.57 in

#### Work Step by Step

we need to find the perimeter of the sector which is nearest hundredth of an inch.
We need to find out the arc length which is formed by sector
In a circle whose circumference is c, the length l of the arc whose degree measure is m is given by
l =$\frac{m}{360}$ * c
= $\frac{80}{360}$ * 2$\pi$r
= $\frac{80}{360}$ * 2$\pi$(9)
l = $\frac{2}{9}$ * 18$\pi$
= 4$\pi$ in
The perimeter of the sector = 2 * radius + length of arc
= 2 * 9 +4$\pi$
= (18 + 4$\pi$) in.
$\approx$ 30.57 in