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A couple thousand years ago a king named Hiero II commissioned a goldsmith to make him a crown of gold, as kings are wont to do. But there was a problem, Hiero II suspected that the goldsmith had cheated him by replacing some of the gold with an equal weight of silver.
Normally this would be easy to figure out, since you could just break the crown open and see. But this crown was a holy object and destroying it would anger the gods, so that wasn’t an option.
Hiero II took this problem to Archimedes to solve. Archimedes was a pretty smart dude, but could this problem be too difficult for even him to solve?
While thinking about this problem Archimedes decided to take a bath, presumably making sure to bring along his rubber duck and body cleaning stick thing.
As he entered the bath he noticed the water level rising and suddenly knew the answer. He suddenly jumped out of the tub and ran through the streets naked screaming “Eureka” (this is an actual part of the story).
What was the solution? While the silver had the same weight as the gold it replaced, silver is much less dense than gold, so would require more volume than the equal weight of gold.
Archimedes discovered that when you place an object in water, the water level rises according to the volume of the object. If he put the crown in a tub of water and it rose too much, that would mean the goldsmith cheated the king.
According to the story, the crown ended up having silver in it, and the king presumably punished the goldsmith who had cheated him.