How Do Big Cruise Ships Stay Afloat On The Sea If They Are So Heavy?

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Water displacement. When the weight of the water the ship displaces is the same as the weight of the ship, the ship floats.
The ship is large but contains a lot of empty space, so it's mass to volume ratio (density) is small, less than or equal to that of water. If the empty space on the ship were to be filled with something, sand for example, it would not float because the weight of the ship would be far greater than that of the water it was displacing.

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