What Archimedes had found was a method for measuring the volume of an irregularly-shaped object. He realised that an object, when immersed in water, displaced a volume of water equal to its own volume, and that by measuring the volume of the displaced water, the volume of the object could be determined, regardless of the object's shape. So, he could measure the volume of the crown by measuring the volume of the water spilled from a container filled with water to the brim when the crown was fully dipped in it.

How then, would this realisation help him to answer Hiero's question - had the goldsmith mixed silver in the golden crown or not? Let us see how Archimedes used his discovery to solve the king's problem.

In physics, when we speak of the density of an object, we are comparing its mass with its volume, or, in simpler words, considering how heavy it is in relation to its size. For example, iron is denser than cork. So a lump of iron is much heavier than a piece of cork of the same size, or much smaller than a piece of cork of the same weight.

Archimedes knew that gold was denser than silver - so a piece of gold weighing a certain amount would be smaller than a piece of silver weighing the same:

Thus, if the goldsmith had stolen some of the gold the king had given him, and replaced it with an equal weight of silver in the crown, then the total volume of the gold+silver crown would be greater than the volume of the original amount of gold.

So now, all that remained for Archimedes to do was to compare the volume of the crown to the volume of the amount of gold that Hiero had given the goldsmith.

  Archimedes and the Golden Crown cont'd... 

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See also:    Who was Archimedes?    |    Who was Galileo?