3. Andrew has two containers for carrying water. The containers are cubes without tops and have base areas of $4 \mathrm{dm}^{2}$ and $36 \mathrm{dm}^{2}$ respectively. Andrew has to completely fill the larger cube with pond water, which must be carried from the pond using the smaller cube. What is the smallest number of visits Andrew has to make to the pond with the smaller cube?
3. $\mathbf{2 7} \mathrm{We}$ first observe that any pair of cubes are mathematically similar. These cubes' surface areas are in the ratio $1: 9$, so that their lengths are in ratio $1: 3$ and that their volumes are in ratio $1: 27$.
Therefore Andrew may fill the larger cube in 27 visits, provided the smaller cube is completely filled on each occasion.