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What makes a ship float?

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How is it that ships made largely of steel can float when the density of steel is much higher than the density of water? Why is it possible to make oil tankers much larger than other ships (and what happens when an oil tanker is unloaded?)

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This solution discusses the reasons why ships float.

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Since a good proportion of the boat is filled with air, as a result, the average density of a boat is a combination of air and steel, ...

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