Answer
We have a solid sphere of radius less than or equal to $1$.
Work Step by Step
Since
$$ x=r\cos \theta,\quad y=r\cos \theta, \quad z=z,$$
then the set $$ x^2+y^2+z^2\leq1$$
takes the form
$$ r^2\cos^2\theta+r^2\sin^2\theta+z^2=r^2+z^2\leq1$$
which is a solid sphere of radius less than or equal to $1$.
