Question

An archeologist finds a 1.62 kg goblet that she believes to be made of pure gold. She determines that the volume of the goblet is 205 mL.

Answer 1

(1620 g) / (205 mL) = 7.90 g/mL
The density of gold is more like 19.3 g/mL, so the goblet is certainly not pure gold -- although it could be made of an alloy containing a little gold, but not much.