A 75 gram bar of gold is cut into three equal pieces. How does the density of each piece compare to the density of the original bar?

1. Each piece is 1/3 the density of the original bar

2. Each piece is the same as the density of the original bar

You should know that density is the relation between, mass and volume as it is described in this equation: d = m/v. As the mass doesn't change in each piece, you will see that volume is less than the original, that's why each piece is 1/3 the density of the original bar or, you can also see, that you have increase by 3, the density original.