An ornament weighs 36 g in air and 34 g in water. The goldsmith claims that no copper or other material has been mixed with the gold, but rather that some cavities might have been left inside the ornament. Determine the volume of the cavities that would account for these weights. The specific gravity of gold is 19.3 .

Step-by-step solution

Weight of the ornament in air = 36 g Weight of the ornament in water = 34 g Loss of weight in water = 36 - 34 = 2 g The loss of weight is equal to the weight of the water displaced. Since the density of water is 1 g/cm ^3 , the total volume of the ornament is: V = 2 cm ^3 The mass of gold in the ornament is 36 g and its specific gravity is 19.3 . The volume of actual gold is: V_ gold = 36 19.3 1.865 cm ^3 The volume of the cavities is the difference between the total volume and the volume of gold: V_ cavity = V - V