Question

Bonus-1 point) According to Vitruvius, a new crown in the shape of a laurel wreath had been made for King Hiero lII, and Archimedes was asked to determine whether it was of solid gold, or whether silver had been added by a dishonest goldsmith. Archimedes had to solve the problem without damaging the crown, so he could not melt it down. While taking a bath, he noticed that the level of the water rose as he got in. He realized that this effect could be used to determine the volume of the crown. By dividing the weight of the crown by the volume of water displaced, its density could be obtained. The density of the crown would be lower if cheaper and less dense metals had been added. Archimedes then took to the streets naked, so excited by his discovery that he had forgotten to dress, crying "Eureka!" "I have found it!" The density of pure gold (24 carat) is 19.32 g/cm The density of 22 carat gold (gold and copper) is 17.90 g/cm The density of 21 carat gold (gold with more copper) is 16.80 g/cm3 The density of 18 carat gold (equal parts gold and cupper) is 15.45 g/cm The density of pure copper is 8.96 g/cm A sample of metal identical to that of the King's crown weighed 29.17 g. When placed in a vessel containing exactly 20.00 mL of water, the water level raised to 21.51 mL. What was the mposition of the King's crown? 24 carat gold 22 carat gold C. 21 carat gold D. 18 carat gold E. pure copper

Answer 1

Thank you vmuch....

Change is volume of water = 21.51 - 20.00 V = 1.51 ml This means the volume of metal placed is also = V = 1.51 cm^3 mass of metal = 29.17g Now density = mass/volume = 29.17/1.51 = 19.317 almostequalto 19.32g/cm^3 d = 19.32g/cm^3 Correct answer (A) 24 carat gold