Find volume of region lying above $z=0$, below $z=4-x^2-y^2$ and inside extruded disc $x^2+y^2=2^2$

Question

I am working on the following homework problem:

Find the volume of the region that lies above the plane $z=0$, below the surface $z=4-x^2-y^2$ and inside the extruded disc $x^2+y^2=2^2$.

I think that, to find the volume, I need to precisely determine the $3$-$d$ region over which I need to integrate.
However, I am struggling to visualise the region.

What might be an effective way of visualising this region properly?

Answer 1

Is it not the extruded disc a cylinder and that $z =4 - x^2-y^2 $ an inverted elliptic paraboloid

Volume $$= \int_{-2}^{2}\int_{-\sqrt{4-x^2}}^{\sqrt{4-x^2}}\int_{0}^{4-x^2-y^2} dzdydx$$ $$= 8\pi$$