Introduction: In the third century B.C., King Hieron of Syracuse asked the famous mathematician Archimedes to determine if his crown was made of pure gold. This was a puzzling problem for Archimedes-he knew how to measure the weight of the crown, but how could he measure the volume? Archimedes solved the problem when he got into his bath and noticed the water spilling over the sides of the tub. He realized that the volume of the displaced water must be equal to the volume of the object placed into the water. Archimedes was so excited by his discovery that he jumped out of the bath and ran through the streets shouting "Eureka!" Question: How can you tell if a crown is made of solid gold? 1. Think about it: Gold is one of the densest substances known, with a density of 19.3 g/cm. If the gold in the crown was mixed with a less-valuable metal like bronze or copper, how would that affect its density? 2. Observe: Drag each of the crowns into the liquid. Based on what you see, which crown do you think is densest? Explain why you think so.