Ask MetaFilter | Community Weblog: "If the tub were submerged up to the brim, it would displace this volume of water. The density of water is 1000kg/m^3, so it weighs 9800N/m^3 or 3.612�10^-2lb/in^3. Therefore the weight of the water displaced is (54672in^3) * (3.612x10^-2lb/in^3) = 1974.7lb. This is much larger than the 340 lb weight of the tub (plus the weight of a passenger), so by Archimedes' Principle, it will easily float. In fact, it will probably be less than halfway submerged."

THIS sort of thing is exactly why ask meta is popular.