Question 200
For each finite subset $F$ of the space $R^3$, define $V_r(F)$ as the union of the open spheres with center on each point of $F$ and radius $r$. Prove that, for $0 \lt r \lt R$,
$$
\mathrm{vol}(V_R(F)) \le \frac{R^3}{r^3} \mathrm{vol}(V_r(F)).
$$
$$
\mathrm{vol}(V_R(F)) \le \frac{R^3}{r^3} \mathrm{vol}(V_r(F)).
$$