Solid gold has a greater density than liquid gold what must happen to the volume of a given mass of solid gold when it becomes a liquid

There's an inverse relationship between density and volume. The higher the density, the smaller the volume occupied because the particles are compact; the lower the density the higher the volume - molecules are further apart. Hence objects with higher densities tend to have small volume but mass doesn't change. Since solid gold has a greater density than liquid gold this means solid gold occupies a smaller volume than the same mass of solid gold. If solid gold changes to liquid, now the particles are further apart and so the volume increases.