A $2.9 \, \text{cm}$ diameter measuring cylinder is filled with water to a height of $4 \, \text{cm}$, then dense copper cubes with an edge length of $2 \, \text{cm}$ are placed into the cylinder. What is the maximum number of cubes that the water in the cylinder can submerge?
Since the face diagonal of the cubes is $2 \sqrt{2} \approx 2.83 \mathrm{~cm}$, which is slightly smaller than the diameter of the cylinder, only one cube can be placed on the base of the cylinder. If we place more cubes in the cylinder, for the same reason, there will be one cube on each level. When $n$ cubes are placed in the cylinder, the height of the structure formed by these cubes is $2 n \mathrm{~cm}$. This structure will be submerged in water if the volume of the part of the cylinder outside the cubes, with a height of $2 n$, is less than the volume of the water in the container:

$$
2 n\left(1.45^{2} \pi-4\right)<4 \cdot 1.45^{2} \pi, \quad \text { i.e., } \quad n<\frac{4 \cdot 1.45^{2} \pi}{2\left(1.45^{2} \pi-4\right)} \approx 5.07
$$

Therefore, at most 5 cubes can be submerged in the water.