Show that the point satisfies the conditions

50 Views Asked by At

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 $$0 \leq r \leq a \ , \ \ 0 \leq \theta \leq 2 \pi \ , \ \ |z| \leq b$$

$$$$

Could you give me some hints how we could show that??

$$$$

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 $b$" ??