Answer
The surface is a cone.
Work Step by Step
In cylindrical coordinates, $r$ is always the distance back to the $z$-axis. Note that for a point in the $yz$-plane, $\left| y \right|$ is the distance back to the $z$-axis. So, in the $yz$-plane, $r$ and $y$ behave similarly. Therefore, we can replace $z=r$ with $z=y$ in the $yz$-plane. This is an equation of the line. Since there is no constraint on $\theta$, we graph this line and rotate it around the $z$-axis to obtain the cone as shown in the figure.
