Introduction: In the 3rd century BCE, King Hieron of Syracuse asked the famous mathematician Archimedes to determine whether 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 bathtub and noticed that the water was spilling over the sides of the bathtub. He realized that the volume of the displaced water must be equal to the volume of the object placed in the water. Archimedes was so excited by his discovery that he jumped out of the bathroom and ran through the streets screaming "Eureka!" Question: How can you tell if a crown is made of pure gold?
PartI. Think about it: Gold is one of the densest substances known, with a density of 19.3 g / cm3. If the gold in the crown were mixed with a less valuable metal like bronze or copper, how would that affect its density? _________________________________________________________________________ _________________________________________________________________________
Part 11. Observe: Drag each of the crowns into the liquid. Based on what you see, which crown do you think is the densest? Explain why you think so. _________________________________________________________________________ _________________________________________________________________________
Part III Measure: Find the mass, volume, and density of each of the three crowns. Crown Mass (g) Volume (cm3) Density (g / cm3) TO 325.2g 62.5cm ^ 3 5.2g / cm ^ 3 B 1264.2g 65.5cm ^ 3 19.3 g / cm ^ 3 C 306.0g 61.6cm ^ 3 4.9 g / cm ^ 3 Part IV Draw conclusions: Which of the three crowns was made of gold? _____________________ Explain: __________________________________________________________________ _________________________________________________________________________