TED-Ed: How taking a bath led to Archimedes' principle - Mark Salata

The video explores moments of perplexity leading to discoveries, focusing on Archimedes, a Greek mathematician. Archimedes was tasked by the king of Sicily to determine if a goldsmith had cheated him by mixing silver into a gold crown. Archimedes discovered the principle of water displacement while taking a bath, realizing it could measure the crown's volume. By comparing the crown's density to pure gold, he confirmed the goldsmith's deceit. This method, now known as Archimedes' principle, demonstrates how water displacement can measure an object's volume.

Explain the significance of density in Archimedes' method for testing the crown.

How did Archimedes determine if the goldsmith had cheated the king?