Find mass of solid bounded by cone $z = 2\sqrt{x^2 + y^2}$ and plane $z=4$

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Let S be the solid bounded by the cone $z = 2\sqrt{x^2 + y^2}$ and plane $z=4$. Let S have mass $m$ and constant density $\rho_0$.

Express $\rho_0$ in terms of $m$ $\\$
Find the moment of inertia of S about the z axis and express it in terms of $m$