Have made a few estimates for a typical 747.
Rough volume of fuselage and wings is 100,000 cubic feet.
If air occupies about 20% of the volume then we end up with about 6000 pnds content of air at sea level.
Using volume of 100,000 and a weight of 450,000 pnds then density is close to 4.5 pnds/cubic foot.
That puts the relative density (to water at 62.5 pnds per cubic foot) at about 4.5/62.5 = 0.07. This is a lot lower than expected perhaps similar to a model made from something lighter than balsa.
Am I close?