A king orders a gold crown having a mass of 0.5 kg. When it arrives from the metalsmith, the volume of the crown is found to be 185 cm3. Is the crown made of solid gold?

The crown is not made of solid gold.  

Explanation:

Density ρ = M/V.  M and V are given.

The density of the crown is (0.5 kg)/(185 cm3) * (106 cm3)/(1 m3) = 2.7*103 kg/m3.

A comet orbits the Sun at an average distance of 70 AU. A comet orbits the Sun with a period of 76 years. It's closest approach to the Sun is 3 AU.