- Why do things float?
- What is density?
I think it’s illegal to write anything about buoyancy without telling the story of Archimedes. So here goes.
Archimedes was a scholar who lived in Greece in the 200s BC. As the story goes, the king of Syracuse gave a local smith some gold and requested that it be turned into a crown. When the crown was finished, the king suspected that the smith had kept some of the gold for himself, replacing the stolen quantity with silver, which was much less valuable. Luckily for the king, there was a person in the kingdom who is recognized today as one of the greatest scientists, mathematicians, and inventors of all time. The king went to Archimedes and asked him to sort out the whole crown situation.
The crown was found to have the correct weight, but the smith could have put in just enough silver to match the weight of the missing gold. However, gold was known to be almost twice as dense as silver – in other words, one piece of gold would weigh about twice as much as an equal-sized piece of silver. So if the smith had indeed cheated, the crown would be bigger than expected – specifically, it would have a greater volume.
But nobody could figure out how to determine the volume of a shape as strange as an intricately-wrought crown. They could melt it and re-shape it into a nice cube (and just multiply length x width x height), but then the crown would be ruined.