Sol. Since the piece of ice containing the lead weighs more than a piece of pure ice of the same volume would do, it sinks lower in the water than the piece of pure ice and displaces a greater volume of water than will be formed as the ice melts (see previous problem). Therefore when the ice melts the level of the water will fall (the piece of lead will then sink to the bottom, but its volume remains the same and it does not directly alter the level of the water).

If there are bubbles of air in the ice, the piece of ice will weigh less than a piece of solid ice of the same volume and consequently it will not sink so deep as a solid piece of ice of the same volume. However, since the weight of the bubble of air can be ignored (by comparison with that of the ice), the piece of ice displaces, as before, the same weight of water as its own weight; when the ice, melts, the level of the liquid will not alter (when the ice melts, any bubbles will rise to the top and leave the water). Therefore the case when a bubble is contained in the ice is not the reverse of the case when lead is contained.