Puzzle answer

The water level lowers. It will be a tiny amount especially if the lake is large. When the cannon ball is in the boat the weight of the ball pushes the boat into the water which raises the water level. The boat with the man in it will take up a certain amount of space that would otherwise be occupied by water. It is a well known principle of science that the cannon ball will cause the boat to take up additional space equal to a volume of water that weighs the same as the cannon ball. Since the cannon ball is much denser than water, that volume of water will be much greater than the volume of the cannon ball. But when the ball is put into the water it takes up a volume of water equal to its own volume. Less space is taken up by the lake, so the water level goes down.

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