I don't understand how the limits of integration have been obtained in the following worked example:

So, how did they get the limits $\displaystyle \int^{2 \pi}_0 \int^1_0 \int^1_r$?

I know that for the double integral they've used polar coordinates. The $\displaystyle \int^{2 \pi}_0 \int^1_0$ represents the unit circle. I tried to sketch the region but I'm not sure how the solid is supposed to look like...

Especially I don't know how they got limits "$\displaystyle \int^1_r$"! Does $\displaystyle \sqrt{x^2 + y^2}$ represent a hemisphere?

I really appreciate it if anyone could explain these to me.