A round membrane in space, is over the space $x^2+y^2 \leq a^2$.
The maximum coordinate $z$ of a point of the membrane is $b$.
We suppose that $(x, y, z)$ is a point of the inclined membrane.
Show that the respective point $(r , \theta , z)$ in cylindrical coordinates satisfies the conditions $$0 \leq r \leq a \ , \ \ 0 \leq \theta \leq 2 \pi \ , \ \ |z| \leq b$$
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Could you give me some hints how we could show that??
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EDIT:
Using cylindrical coordinates we get $r=\sqrt{x^2+y^2}=\leq |a|$ and sonve $r \geq 0$ we have $0 \leq r \leq a$.
From the defintion of cylindrincal coordinates we have that $0 \leq \theta \leq 2 \pi$,
But how do we get that $|z| \leq b$?? By the sentence "The maximum coordinate $z$ of a point of the membrane is $b$" ??