Ok My previous considering the level of the water didn?t impress any body Now we have the ice cube containing the air bubble and now if the ice block melts then the water level will remain at the same level. This is because the volume of the water that was displaced is exactly equal to the volume of water that came in. This is because the air after melting doesn?t displace any fluid. Now for a example consider the situation where the air bubble is replaced with a heavy metal (such the rho>rho(water) ) Now the volume displaced by the metal is more than that of the volume displaced by the ice cube. Therefore the level of water decreases.
I still remember that my prof handed out this problem and he asked me solve it.
So therefore the ans: The level of the liquid doesnot falls or rise but rather remains the same
This was the question given to me in one of the exams ---Hope this Helps