Mastering chemistry if the new ring is indeed pure platinum (density = 21.4 g/cm3), what is its mass?

Well, for this problem, you know that even from the units of density, that it is the ratio of a substance's mass to its volume. With the given density, you have to know the volume in order to determine the mass. But since no information about the volume is given, I can't give you an exact numerical answer. The closest answer I could give is an algebraic equation in terms of volume, V.

Density = Mass/Volume

Mass = Density*Volume

Mass = 21.4V

where mass is in grams and V is in cm³