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

Answer 1

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.

Answer 2

Look up "hydrostatic principle" for details.