A solid cube just gets completely immersed in water when a 0.2 kg mass is placed on it. If the mass is removed, the cube is 2 cm about the water level. What is the length of each side of the cube?

Let the side of the cube be L centimeters. When the 0.2 kg mass is removed, the cube rises by 2 cm. This means that the weight of the 0.2 kg mass was exactly equal to the weight of the water displaced by that 2 cm height of the cube. According to Archimedes Principle, the weight of the added mass equals the weight of the water displaced by the volume that submerged because of that mass. The volume of the water displaced by the 2 cm height is the area of the base times the height, which is L times L times 2 cubic centimeters. The mass of water displaced is its volume multiplied by its density. Since the density of water is 1 gram per cubic centimeter, the mass of the displaced water in grams is 2 times L squared. The mass placed on the cube was 0.2 kg, which is 200 grams. Setting the mass of the displaced water equal to the added mass: 2 times L squared equals 200. L squared equals 100. L equals 10. Therefore, the length of each side of the cube is 10 cm. Correct Answer: B