I have used the gold you gave me. Here is the crown.
I heard that the goldsmith cheated the King!
Help me find out if the crown is gold or not.
Hiero, the new King, wanted a crown to be made in honour of his victory. The crown had to be pure gold and in the shape of a laurel wreath.
The King gave some gold to the goldsmith and asked him to fashion a crown for him. A few days later, the goldsmith returned with what the King had asked for.
We just need to put the crown in a tub of water.
The King heard that the goldsmith had cheated him of the gold in his crown and secretly put some silver in instead. He called Archimedes to help him find out the truth.
I have found that, the crown displaced more water than the lump of gold I tested.
I therefore believe that the crown is not pure gold. The goldsmith is guilty of cheating the King!
Archimedes was sitting in the bath when he found that as he lowered himself into the bath, the water spilled over. The further down he went, the more water spilled over. He had found the solution to Hiero's problem!
Archimedes had found a method for measuring irregular-shaped objects. He could measure the volume of the crown by measuring the volume of water of the water spilled from a container filled with water.
Archimedes knew that gold was denser than silver, so a piece of gold weighing a certain amount would be smaller than a piece of silver weighing the same. The total volume of the gold and silver crown would be greater than the total volume of the original amount of gold.