Answer
$27 \pi \ m$
Work Step by Step
Let $l$ be the length of an arc:
$l=\dfrac{\text{Measure of the arc}}{360^{\circ}} \times 2 \pi r ~~~(a)$
or, $l=\dfrac{\text{Measure of the arc}}{360^{\circ}} \times \pi d~~(b)$
Here, $r$ represents radius and $d$ is diameter.
$360^{\circ}-90^{\circ}=270^{\circ}$ and $r=18 \ m$
Thus, equation (a) becomes:
$l=\dfrac{270^{\circ}}{360^{\circ}} \times 2\pi (18)=27 \pi \ m$