1. First he woke up in the morning.
2. He said "EUREKA!" and understood how some of the objects float and others don't.
3. He went to the local museum and asked if his body could be buried under it.
(This, sadly, wasn't possible and so he is buried in a normal chest).
4. Then he died a few years later, having so many secrets that no-one knows how he actually revealed the way he discovered his principle.
Too bad for you, hun.
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According to Vitruvius, a new crown in the shape of a laurel wreath had been made for King Hiero II, and Archimedes was asked to determine whether it was of solid gold, or whether silver had been added by a dishonest goldsmith. Archimedes had to solve the problem without damaging the crown, so he could not melt it down into a regularly shaped body in order to calculate its density. While taking a bath, he noticed that the level of the water in the tub rose as he got in, and realized that this effect could be used to determine the volume of the crown. For practical purposes water is incompressible, so the submerged crown would displace an amount of water equal to its own volume. By dividing the weight of the crown by the volume of water displaced, the density of the crown could be obtained. This density would be lower than that of gold if cheaper and less dense metals had been added. Archimedes then took to the streets naked, so excited by his discovery that he had forgotten to dress, crying "Eureka!" (meaning "I have found it!")
In the history of science, Archimedes is credited with being the first to state the
physical law that a body in fluid is buoyed up by a force equal to the weight of
the displaced fluid.
He didn't discover volume. He pointed out that the weight of a liquid displaced by a floating body was equal to the weight of that body (Archimedes' Principle).
According to legend, he discovered buoyancy when he got into a bathtub and noticed how the water rose as he got in. He then shouted 'Eureka!', and ran through the streets naked.