Question

if steel is more dense than lake water, why can a boat float?
the average density of the boat, including the steel and air, is less dense than 1.00 g/cm³
the average density of the boat, including the steel and air, is more dense than 1.00 g/cm³
lake water is more dense than pure water
steel has a special ability to float regardless of density

Explanation:

According to Archimedes' principle, an object floats when its average density is less than the density of the fluid it is in. For a boat, although steel is dense, the air inside the boat (hollow parts) lowers the average density. Lake water's density is around \(1.00\ g/cm^{3}\). If the boat's average density (steel + air) is less than \(1.00\ g/cm^{3}\), it floats. The option about lake water being more dense than pure water is incorrect as lake water's density is close to pure water (and even if it were, it's not the reason for the boat floating here). Steel has no special floating ability regardless of density. And if the boat's average density were more than \(1.00\ g/cm^{3}\), it would sink.

Answer:

The average density of the boat, including the steel and air, is less dense than \(1.00\ g/cm^{3}\)