Achimedes is said to have curried favor with a king by determinning that a crown the king had commissoned was not pure gold. Explain in detial how he could have done this

It had to do with the specific weight of gold and the silver that was used as a substitute for some of the gold.

Legend has it, that it actually was a wreath and not a crown.

Look up "hydrostatic principle" for details.

To determine whether the crown was made of pure gold, Archimedes likely used a method called buoyancy. Let me explain how he could have done this:

1. Archimedes needed to know the density of pure gold. He would have measured the weight of a known volume of pure gold to determine its density.

2. The next step for Archimedes would be to measure the weight of the crown in question. If the crown was made of pure gold, it should have the same weight as an equal volume of pure gold.

3. Archimedes would then need to find the volume of the crown. This is where the principle of buoyancy comes into play. He would have placed the crown in a container filled with water and carefully collected the water that overflowed.

4. The displaced water would be equal in volume to the crown. Archimedes would measure the volume of the water he collected after immersing the crown in the container.

5. By comparing the weight of the crown to the weight of an equal volume of pure gold, Archimedes would be able to determine if the crown was made of pure gold or if some other material, such as a less dense metal, was mixed in.

If the weight of the crown was less than that of the same volume of pure gold, it meant that the crown had a lower density due to the presence of another material. Consequently, if the weight of the crown was the same as an equal volume of pure gold, it was likely made of pure gold.

It is said that Archimedes made this discovery while taking a bath and observing the water overflowing. He was so overjoyed with his findings that he ran through the streets of Syracuse, shouting "Eureka!" which means "I have found it!" in Greek.