Finding the volume using spherical coordinates

Question

I am stuck on the limits of integration for rho. I tried 0 but that didn't work. Is this because I'd be finding the area under the $z=2$ plane?

Question: Write a triple integral including limits of integration that gives the volume of the cap of the solid sphere $x^2+y^2+z^2\le 8$ cut off by the plane $z=2$ and restricted to the first octant.

Answer 1

Hint. From the diagram, the minimum $\rho$ value is given by $$\rho_{\rm min}\cos\phi=2\ .$$