Final answer:
The density of one of the pieces of a broken aluminum cube would be the same as the entire cube, since density is an intensive property that does not change with the size of the sample. Aluminum's density is consistently 2.70 g/cm³.
Step-by-step explanation:
When a cube of aluminum is broken into many irregularly shaped pieces, the density of one of the pieces would be the same as the density of the entire cube. This is because density is an intensive property, meaning it is independent of the size of the sample. The density of pure aluminum is always 2.70 g/cm³ at 20°C, regardless of the size of the sample.
To further illustrate, if you have a 100-gram hollow cube made of aluminum foil with a known surface density of 15 g/cm², the side length of such a cube can be calculated by considering that the surface area required to create this cube, based on its mass and surface density, would be the total area of all six sides. This demonstrates that while surface area and mass may change when altering the size or shape of an aluminum sample, the density remains constant.
Thus, breaking a cube of aluminum into smaller pieces does not change the mass-to-volume ratio, and hence the density remains 2.70 g/cm³.