KöMaL 2007 K142

In the Mathematical Olympiad of 2100, gold and silver medals will be made of pure gold and silver (and bronze medals will be made of bronze). The diameter of the silver medal will be 3 cm, with a thickness of 5 mm. (The shape of the medals will be as usual.) What will be the diameters of the gold and bronze medals if all the three kinds of medal have the same mass and thickness? (Densities: gold $19 300~\rm kg/m^{3}$, silver $10 500~\rm kg/m^{3}$, bronze 8930 $kg/m^3$.)