Answer
$3 \pi \ m$
Work Step by Step
$l=\dfrac{\text{Measure of the arc}}{360^{\circ}} \times 2 \pi r ~~~(a)$
or, $l=\dfrac{\text{Measure of the arc}}{360^{\circ}} \times \pi d~~(b)$
Here, $r$ represents radius and $d$ is diameter.
We are given that the red arc measures $180^{\circ}-90^{\circ}=90^{\circ}$ and $r=6 \ m$
Thus, equation (a) becomes:
$l=\dfrac{90^{\circ}}{360^{\circ}} \times 2\pi (6)=
3 \pi \ m$
