Probably should include what problem Archimedes has been stuck on until his realization of the principles of buoyancy gave him a solution.
The King had order a gold crown, and after receiving it suspected that the goldsmith may have replaced some of the gold with cheaper silver. The King asked Archimedes to figure out if the crown was pure gold.
Archimedes could do that by figuring out its density, but to do that he needed to get the weight of the crown and the volume of the crown. Weight was easy, but he had no idea how to get the volume, other than melting it down and reshaping it into a shape whose volume he could calculate. Naturally, the King wanted Archimedes to answer the question without destroying the crown.
His realization that the volume of water displaced by an object that is more dense than water is equal to the volume of the object gave him a way to get the volume of the crown without harming it.
The King had order a gold crown, and after receiving it suspected that the goldsmith may have replaced some of the gold with cheaper silver. The King asked Archimedes to figure out if the crown was pure gold.
Archimedes could do that by figuring out its density, but to do that he needed to get the weight of the crown and the volume of the crown. Weight was easy, but he had no idea how to get the volume, other than melting it down and reshaping it into a shape whose volume he could calculate. Naturally, the King wanted Archimedes to answer the question without destroying the crown.
His realization that the volume of water displaced by an object that is more dense than water is equal to the volume of the object gave him a way to get the volume of the crown without harming it.