Who can you find the limits

Hello,

I will calculate the follow surface integral but before I need to find the limits but that's the problem I had now idea.

$\displaystyle \left\{ \begin{array}{l} x =\varphi cos( \theta) \\ y=\varphi sin( \theta) \\ z=c \theta \end{array} \right. $

In the first octant between two cilinders $\displaystyle x^2+y^2=a^2$ and $\displaystyle x^2+y^2=a^2$

I think that the angle $\displaystyle \theta$ must be between $\displaystyle 0<=\theta<=\frac{\phi}{2}$

But who can I find the rest? what type of coordinates do I prefer?

Greets. Thanks.