Volume of a solid bounded by a paraboloid and the x-y plane

[NZBRU]

Homework Statement

So I am trying to accomplish the above by using spherical coordinates, I am aware the problem may be solved using dv=dxdydz= zdxdy were z is known but I would like to try it using a different approach (using spherical coordinates). Any help would be greatly appreciated

Homework Equations

The Attempt at a Solution

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[blue_leaf77]

Judging from the integration limit, it can already be seen that your approach is misleading. In fact, you are just calculating the volume of a sphere of radius $\sqrt{3}$.
Use cylindrical coordinate instead.