Archimedes was a Greek mathematician, physicist and inventor. He lived in Syracuse in around 200 BC.
I know, I'll find out how much water is displaced by lumps of gold and silver
The King had ordered a blacksmith to make him a gold wreath only out of pure gold. The King was pleased until rumors had started to appear saying that the goldsmith had cheated the King. So, he ordered Archimedes to find out the truth.
The king has been cheated!
One day Archimedes walked to the public baths and as he got in he realised that as he began to lower himself into the water, it began to spill out over the sides. Archimedes continued to lower himself slowly into the water, and he noticed that the more his body sank into the water, the more water ran out over the sides of the tub. He had found the solution to the Kings problem.
I knew it!
He realised that an object when put in water displaced a volume of water equal to its own volume and by measuring the volume of the displaced water, the volume of the object of the object could be found. So to find out if the goldsmith had cheated the King, he put gold and silver into different buckets to find their individual volumes.
He then measured the density of the crown to see if the goldsmith had mixed silver and gold in the crown. 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 and silver crown would be greater than the original volume of gold.
Archimedes found that the crown did displace more water than the lump of gold of the same weight. He came to the conclusion that the crown was not pure gold and that the goldsmith had mixed some silver (or other lighter metal) into the gold in an attempt to cheat the King.