How do you set up the integral in spherical coordinates in the following problem?

How do you set up the integral in spherical coordinates in the following
problem?

Find the volume bounded by the surface $z^2 = x^2 + y^2$ and $x^2+y^2 =
1$. The answer is $\pi/8$ using rectangular and cylindrical coordinates,
but it is $\pi/24$ when I switched to spherical coordinates, as follows,
$$\int_0^{\pi/2} \int_{\pi/4}^{\pi/2} \int_0^{\cot{\phi} \csc{\phi}}
\rho^2 \sin{\phi} \, d\rho \, d\phi \, d\theta.$$ In general, how do you
figure out the bounds for $\theta, \rho$ and $\phi$? I use the conversion
formulas but I'm not sure how to proceed in a general way.
Also, how to you finish a paragraph and enter onto the next line when you
edit this (I'm new to this site)? Thanks a lot!