The story of scientist in a bath tub

Once upon a time, the King of Syracuse, ordered a goldsmith to make a golden crown.The King gave a piece of pure gold to the goldsmith for this purpose. In a short time the crown was ready. But when it was presented to the King he became suspicious. Was the crown made of pure gold? He summoned Archimedes, a mathematician, and asked him to solve the problem. Archimedes was in deep thought. Both the crown and the piece of pure gold weighed equal. Then how to ascertain the purity of the crown without breaking it? One day as Archimedes entered the bathtub, water spilled out of it. All of a sudden he got an idea and he shouted happily ‘Eureka…I have found it’. Now lets understand, how Archimedes solved the problem. He noticed that the amount of water spilled out of the bathtub was equal to the volume of his body. Thus, he concluded, that any object when put in water would displace an amount of water equivalent to its mass. Then he calculated the volume of the crown by marking the rise in water level, when it was put in a container filled with water. Next he took a piece of pure gold weighing same as the crown and put it in water. This time the rise in water level was lesser. Hence it was proved that the crown was not made of pure gold. In fact, Archimedes had unknowingly calculated the density of the two objects. Let me explain it to you. Archimedes reasoned that any object when put in water would displace a volume of water in relation to its mass. Today, we know that mass per volume gives the density of an object. If any object has silver mixed with gold then its density will be more than a piece of pure gold. Addition of silver had increased the density of the crown, and thus, it displaced more water than a piece of pure gold.

Web references :

Archemedies
Archimedes and the Golden Crown
Principals Of Buoyancy