Answer
Please see the figure attached.
Work Step by Step
In cylindrical coordinates, $r$ is always the distance back to the $z$-axis. Thus, $r \le 3$ corresponds to a disk of radius $3$. Since the $z$-coordinate is the same as in rectangular coordinates, the disk is located at height $z=4$. However, since $\theta$ is constrained in the interval $\pi \le \theta \le \frac{{3\pi }}{2}$, the region is located in the third quadrant.
