Solution
= Solution
Scale the unit ball by $(u,v,w)\mapsto(au,bv,cw)$. Symmetry makes all products of inertia vanish, while the unit-ball averages satisfy
$\langle u^2\rangle=\langle v^2\rangle=\langle w^2\rangle=1/5$. The <inertia tensor> about the centre is therefore
$$
\boxed{I=\frac M5
\begin{pmatrix}
b^2+c^2&0&0\\
0&a^2+c^2&0\\
0&0&a^2+b^2
\end{pmatrix}}.
$$