Need help with a basic physics problem.?

Question

A major motor company displays a die-cast model of its first automobile, made from 9.35 kg of iron. To celebrate its one-hundredth year in business, a worker will recast the model in gold from the original dies. What mass of gold is needed to make the new model?

Answer 1

The easiest way to calculate this is to use specific gravity.

SG of gold = 19.32

SG of iron = 7.894

9.35 kg / 7.894 = x kg / 19.32

9.35 kg * 19.32 / 7.894  =  x kg =

22.88 kg

Gold is heavier than iron, therefore the mass of the gold cast must be greater than the mass of the iron cast. The volume is the same.

Answer 2

The density of Fe is 7.87 g/cm³.

The density of Au is 19.32 g/cm³.

The mass of gold required is thus ( 9.35 kg ) ( 7.87 / 19.32 ) = 3.81 kg.