Calculate moment of inertia for Oz axis of solid described by $ \sqrt{x^2+y^2} \leq z \leq \sqrt{R^2-x^2-y^2} $

Question

$$ \sqrt{x^2+y^2} \leq z \leq \sqrt{R^2-x^2-y^2} $$

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Calculate moment of inertia for Oz axis of solid described by expression above.

$$ \int_0^{\frac12R\sqrt2}\int_0^{2\pi}\int_z^\sqrt{R^2-z^2}r^3\,dr\,dx\,dz \,\frac{1}{\int_0^{\frac12R\sqrt2}\int_0^{2\pi}\int_z^\sqrt{R^2-z^2}r\,dr\,dx\,dz} = \frac{R^2}{2} $$

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This is what I ended up doing. My final result is $\frac{MR^2}{2}$ where $M$ is the mass of solid. However this doesn't seem to be the right answer. What is the proper way to find the moment of inertia of this solid?