Archimedes and the Golden Crown
DISCOVERY OF ARCHIMEDES PRINCIPLE-THE GOLDEN CROWN
The most famous about Archimedes is the story of the Golden crown. One day Archimedes was summoned by the king of Sicily to investigate whether he had been cheated up by a goldsmith. The king said he had given the exact amount of gold needed to make the crown, when the crown was ready the king suspected that the goldsmith cheated. The king asked Archimedes to solve the problem without causing damage to the crown. One day while taking bath he noticed when he immersed himself into the tub, the water level raised how much water was displace depended on how much his body was immersed. This excited him so much he ran into the streets nakedly shouting Eureka I found it.

Archimedes checked the density of the crown and the amount of gold immersed in water later they found that the goldsmith had cheated them.
Archimedes Principle
When a body is immersed partially or fully in a fluid it experiences an upward force that is equal to the weight of the fluid displaced by it.
This upward force is called the buoyant force and the property of the fluids to apply buoyant force is called buoyancy.
Application of Archimedes principle
Used in designing ships and submarines
Used in Hydrometer to determine the density of water(liquids)
Used in Lactometer to determine the purity of milk