Answer
Please see the figure attached.
Work Step by Step
In cylindrical coordinates, $r$ is always the distance back to the $z$-axis. Thus, $1 \le r \le 3$ corresponds to the region outside of a circle of radius $1$ and inside of a circle of radius $3$. Since the $z$-coordinate is the same as in rectangular coordinates, $0 \le z \le 4$ corresponds to region between the plane at height $z=0$ and the plane at height $z=4$. So, it is a cylinder. However, since $\theta$ is constrained in the interval $0 \le \theta \le \frac{\pi }{2}$, the region is located in the first quadrant.
