Did Archimedes Use His Principle To Solve King Hiero's Problem?

A man named Hiero was chosen to be the king for the people of Syracuse. He decided to show his honor to the Gods by getting a wreath shaped crown made of pure gold. After inspecting the finished crown, Hiero was satisfied with the goldsmith. King Hiero later found out that the crown may not have been of pure gold, but made of a gold and silver mix. Hiero called in a young man by the name of Archimedes because he was capable of revealing the truth.
How did Archimedes use his principle to solve King Hiero’s problem? One day, while Archimedes was getting into the bath tub, he noticed that the more he walked into the tub, the more water that ran out of the tub. He found out that when an object is immersed under water, there is a volume