= Solution
For a thin uniform <spherical shell>, $dC=(R\sin\theta)^2dm$ and angular averaging gives $\langle\sin^2\theta\rangle=2/3$. Thus $\boxed{C=2MR^2/3}$. The printed formula requires a negligibly thin outer shell. For a \i[finite-thickness] hollow sphere of <uniform density> between $r_0$ and $R$,
$$
C=\frac25M\frac{R^5-r_0^5}{R^3-r_0^3}.
$$
For example $r_0=R/2$ gives $C/(MR^2)=31/70$, not $2/3$. The thin-shell limit $r_0\to R$ restores the printed result. A uniform outer layer of unspecified thickness does not by itself establish it.
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