Consider a paraboloid $x^2+y^2+2=z$. The task is to find the volum of the body obtained by confining the paraboloid by several planes $x=0, z=0, y=0$ and $x=3, y=3$.
The zero planes cuts out a quarter of the paraboloid and the remaining plans cuts out two pieces with crosssections being area of the parabol.
I know how to calculate the volumes, it isn't my problem. The problem is that the answer given is 72. But the way I see it, the confined body is not finite, it's infinite and the volume in this case should be infinite. To make it finite one needs aditional plane, e.g. z=10. I think I am right and the answer given is wrong, but I need reassurance ("another pair of eyes").