Since 1982 pennies have been made of zinc plated with a thin layer of copper. The modern penny weighs 2.500g, has a diameter of 19.05 milliliters and an average thickness of 1.224 milliliters. Given that the density of copper is 8.96 g/cm^3 and the density of zinc is 7.13 g/cm^3, determine the percentage by mass of copper in a modern penny.
Density = Mass / Volume The penny's volume = pi x r^2 x h radius = diameter / 2 = 19.05 / 2 millimetres = 9.525 millimetres = 0.9525 centimetres height = thickness = 1.224 millimetres = 0.1224 centimetres = 3.142 x 0.9525^2 x 0.1224 = 0.3489 cm^3 Overall density of penny = 2.500 / 0.3489 = 7.165 g / cm^3 7.165 x 100% of penny's weight = 7.13 x (% of zinc in penny) + 8.96 x (% of copper in penny) % of zinc in penny + % of copper in penny = 100 therefore % of zinc in penny = 100 - % of copper in penny therefore 7.165 x 100% of penny's weight = 7.13 x (100 - % of copper in penny) + 8.96 x (% of copper in penny) let % of copper in penny = A therefore 7.165 x 100 = 7.13 x (100 - A) + 8.96 x A 716.5 = 713 - 7.13A + 8.96A 3.5 = 1.83A, therefore A = 3.5 / 1.83 = 1.91% copper Total weight of penny = 2.5 grams Total proportion of copper in the penny = 2.5 grams x 1.91 / 100 = 0.04775 grams
