You purchase a rectangular piece of metal that has dimensions 5.0 X 15.0 X 30.0 mm and mass 0.0158 kg. The seller tells you that the metal is gold. To check this, you compute the average density of the piece. What value do you get? Were you cheated?

Solution 3E Density() of the rectangular piece of metal can be calculated using the relation M = V M is mass of the rectangular piece of metal = 0.0158 kg V is volume of the metal = (5.0 × 10 3 × 15.0 × 10 3× 30.0× 10 3 ) m 3 9 3 = 2250× 10 m 0.0158 = 2250×109 3 3 = 7.02× 10 kg/m The density of gold is 19.3× 10 kg/m 3 Therefore,the rectangular piece of metal is not pure gold. The average density is only 36% that of gold, so at most 36% of the mass is gold.