Answer
An infinitely long solid circular cylinder with radius 3 centered at the y-axis.
Work Step by Step
The given inequality does not include $y$, so $y$ can take on every possible value. This means that the region will extend infinitely along the y-axis. At any fixed value of $y$, say $y = k$, we recognize $x^{2}+z^{2} \leq 9$ to represent all the circles k units in front of the xz-plane, with radius less than or equal to 3 and center (0, k, 0). These circles put together make one shaded-in circle. Therefore, our region will be made up of infinite copies of this shaded-in circle, one for every value of $y$. This makes an infinitely long solid circular cylinder with radius 3 and the y-axis as its central axis.
