I cannot work out the last part (iii) All other parts have been solved.
The Attempt at a Solution
From part (ii) I found the new height of the water, and therefore the volume of water and air in the vessel. The Pressure of the water P1 cant be found using; rho.g.h+Patmos(for the water) and you know that P2 of the water is going to be Patmos.
Because you have 2 unknowns for the air, surely you must use V2=(P1V1/P2) However, this yields a greater volume that started with, indicating that the height has increase, not gone done, which is what does happen.
Bet its a really simple solution, but ive been on it for about 3 hours.