This illustrates the fact that the cylinder $C$ is homeomorphic to
the annulus $A$, where
\begin{align*}
C &= \{(x,y,z)\in\mathbb{R}^3\;|\;x^2+y^2=1,\quad -1\leq z\leq 1\} \\
A &= \{(x,y)\in\mathbb{R}^2 \;|\; \tfrac{1}{2} \leq
\sqrt{x^2+y^2} \leq \tfrac{3}{2} \}
\end{align*}
A homeomorphism $f\colon C\to A$ is given by
$$ f(x,y,z) = ((1+z/2)x,\;(1+z/2)y). $$