Calculating the center of mass of a body in $\mathbb{R^3}$

Question

I want to calculate the center of mass of the body defined by $$\begin{cases} x^2+4y^2+9z^2\leq 1 \\x^2+4y^2+9z^2\leq 6z \end{cases}$$ where the density of mass is proportional to the distance to the plane $xy$. First of all I will have to calculate the mass, meaning I have to solve $$M=\iiint dm=\iiint_V \lambda z dV$$ My problem is that I don't know what to do when the body is given in that way, I've done similar problems where it was clear I had to do a change of coordinates (spherical, cylindrical...) however in this case I don't know how to set the integral.