Math Help - Who can you find the limits

1. 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.

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

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

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

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

Greets. Thanks.

2. small mistake between two cilinders namely $x^2+y^2=b^2$ and $x^2+y^2=a^2$