According to legend, a king requested that the royal scientist, Archimedes, determine if his crown was really made of pure gold.

Question

Archimedes measured the mass of the crown and found it to be 505.43 grams. Using volume displacement, he found the volume to be 44mL. What was the density of the crown? Is the crown made of pure gold? (The density of pure gold is 19.3 g/cm^3)

Answer 1

The density of the crown was 505.43 g/44 ml = 11.49 g/ml

The crown was not made of pure gold, for if it were, the density of the crown would have been 19.3 g/ml.

Answer 2

ρ = m/V = (505.43 g) / (44 mL) ≅ 11.487 g/cm³ < 19.3 g/cm³

 

It is not pure gold.