Carla is right. Take each dust grain and colour all points in a distance of at most $2$ cm and at least $1$ cm from the grain. Then we have coloured a volume of $1000 \cdot \frac{4}{3} \cdot \pi \cdot (2^3 - 1^3) = \frac{28000}{3}\pi\text{cm}^3 > 28000\text{cm}^3$ counted with multiplicity. All the coloured points are contained in a $14\text{cm} \times 14\text{cm} \times 14\text{cm}$ box of volume $14^3 = 2744\text{cm}^3$. Hence there is a point that is coloured at least $10$ times, and then there are at least $10$ points in a distance of at most $2$ cm and at least $1$ cm from this point.