There are many stories about how and why Archimedes came up with his many inventions. Several of them tell how King Hiero II would request Archimedes to solve different problems. Archimedes would then go off and come up with some ingenious way to help out the king. One day the king received a new crown made from pure gold. However, he suspected that the goldsmith may have used some silver in the crown to save money. He asked Archimedes to figure out if it was pure gold. Archimedes wasn't sure what to do. He knew the density of gold and the density of silver, but how could he determine the volume of the crown? He figured it out while taking a bath. He could measure the amount of water the crown displaced and then he could compare that with the weight of the object. Once he had this information, he could determine if the density of the crown matched with pure gold.
The real story behind Archimedes' eureka (4:42)
TED-Ed - YouTube
Archimedes principle - Class 9 tutorial (4:35)
amritacreate - YouTube
Buoyancy is the tendency of an object to float in a fluid. All liquids and gases in the presence of gravity exert an upward force known as the buoyant force on any object immersed in them. Buoyancy results from the differences in pressure acting on opposite sides of an object immersed in a static fluid. Watch the video 'Archimedes Principle' and you will the understand the law of Buoyancy.