## Calculus (3rd Edition)

Solid cylinder of radius $1$ centered at the $z$-axis.
Since $$x=r\cos \theta,\quad y=r\cos \theta, \quad z=z,$$ then the set $$x^2+y^2\leq1$$ takes the form $$r^2\cos^2\theta+r^2\sin^2\theta=r^2\leq1$$ which is a solid cylinder of radius $1$ centered at the $z$-axis.