Numbers are only ballpark, because who outside Boeing would know the volume of a 747. Could submerge a model in a bucket and measure displacement I suppose. What we really need is a 3 dimensional cumputer model of the aircraft ! Back to Boeing.
I estimated 2,600 cu.metres, not far from Milt's 100,000 cu.ft.
Based on (round number) MTOW of 400 tonnes, this gives about 150 kg/cu.metre (about 9 lb/cu.ft). Density relative to water of 0.15
For comparison, polystyrene foam is about 50 kg/cu.metre (about 3 lb/cu.ft). Balsa ranges from 3 to 30 lb/cu.ft
I think Milt's figure for air volume of 20% is a bit low. Maybe more like 40% when you consider how much of the PAX and freight space is air. Using 0.9 kg/cu.metre (air at 8,000 ft) I get about 1 tonne of air.
Milt, within the accuracy of all our guesses, you're not far off the mark. Obviously using MTOW or empty weight makes a big difference.
I hope someone finds all this info interesting !
Spec.