Answer
Please see the figure attached.
Work Step by Step
In spherical coordinates, $\rho$ is the distance back to the origin. Thus, $\rho \le 2$ describes a ball of radius $2$. While $\theta$ is the polar angle of the projection $Q$ of a point $P$ onto the $xy$-plane; and $\phi$ is the angle of declination, which measures how much the ray through a point $P$ declines from the vertical. Since $0 \le \theta \le \frac{\pi }{2}$ and $\frac{\pi }{2} \le \phi \le \pi $, we obtain a part of the ball below the first quadrant of the $xy$-plane as is shown in the figure.
