Consider a Sphere of mass $M$, and volume $V = \frac{4}{3}π(r)^3$ and uniform density $p$, If I want to get its moment of inertia around an axis running through its centroid then I shall Integrate $dm r^2$.
And If I cut the Sphere into infinitesimally small volumes of spheres I get $dV = 4πr^2 dr$, $dm = p dV$.
So I get to integrate $p.4πr^4 dr$ from zero to the whole radius if the Sphere, now the final result is $\frac{3MR^2}{5}$ and that's $1.5$ times the real moment if inertia. So what did I do wrong?