Finite-thickness hollow-sphere moment of inertia
= Finite-thickness hollow-sphere moment of inertia
{title2=$C=\frac25M\frac{R^5-r_0^5}{R^3-r_0^3}$}
Integrating $dC=(2/3)r^2dm$ over a uniform-density spherical layer gives the displayed result. It becomes $2MR^2/5$ for a solid sphere and tends to $2MR^2/3$ only in the thin-shell limit. Calling a layer hollow does not make its thickness negligible.