To find the mass of the cube, we can use the fact that it floats so that it is 75% in the water and 25% in the oil. When 75% of the cube is in water, it displaces a volume of 2058 cm³ of water. When 25% of the cube is in oil, it displaces a volume of 686 cm³ of oil. The total mass of the cube is calculated by adding the mass of water and the mass of oil displaced by the cube.
To find the mass of the cube, we need to understand buoyancy. Buoyancy is the force experienced by an object submerged in a fluid. It is equal to the weight of the fluid displaced by the object. In this case, the cube is floating between water and oil with a density of 810 kg/m³.
To calculate the mass of the cube, we can use the fact that it floats so that it is 75% in the water and 25% in the oil. Since water has a density of 1000 kg/m³, the density of the cube must be less than that for it to float. Let's assume the cube has a density of ρ kg/m³.
When 75% of the cube is in water, it displaces a volume of 14.0 cm × 14.0 cm × 10.5 cm = 2058 cm³ of water. This volume of water has a mass of 2058 cm³ × 1000 kg/m³ = 2058 kg.
When 25% of the cube is in oil, it displaces a volume of 14.0 cm × 14.0 cm × 3.5 cm = 686 cm³ of oil. This volume of oil has a mass of 686 cm³ × 810 kg/m³ = 556260 kg.
Since the total volume of the cube is (14.0 cm)³ = 2744 cm³, and the cube is made up of 75% water and 25% oil by volume, we can calculate the total mass of the cube as:
Total mass of cube = (0.75 × 2058 kg) + (0.25 × 556260 kg) = 1468 kg + 139065 kg = 140533 kg
Therefore, the mass of the cube is approximately 140,533 kg when expressed using two significant figures.