A not-too-honest citizen is thinking of making bogus gold bars by first making a hollow iridium ( \(S=22.5)\) ingot and plating it with a thin layer of gold \((S=19.3)\) of negligible weight and volume. The bogus bar is to have a mass of \(100 \mathrm{lbm}\). What must be the volumes of the bogus bar and of the air space inside the iridium so that an inspector would conclude it was real gold after weighing it in air and water to determine its density? Could lead \((S=11.35)\) or platinum \((S=21.45\) ) be used instead of iridium? Would either be a good idea?