# triple integration to find volume

how can I solve this problem I already have the final answer but I don't know how to solve it , the answer for this problem is $$(V=8(pi-1/3)$$ I tried solving it with this:

$$\int_{-2}^2\int_{-\sqrt{4-x^2}}^{\sqrt{4-x^2}}\int_0^{x^2+y^2}dzdydx$$

but it didn't work

Write an iterated triple integral in the order dzdydx for the volume of the region bounded below by the xy-plane and above by the paraboloid $$z = x^2 + y^2$$ and lying inside the cylinder $$x^2 + y^2 = 4$$?

You should switch to cylindrical coordinates instead. Your integral will change to: $$4 \int_0^2 \int_0^{\pi/2} \int_0^{\rho^2} \rho dz d\phi d\rho$$