Final answer:
The distance from the top of the wood to the water surface is 0.09 m, calculated by using the principle of buoyancy which states that the weight of the water displaced is equal to the weight of the cube, considering the cube's density and the volume submerged.
Step-by-step explanation:
The student's question relates to the concept of buoyancy and Archimedes' Principle, which states that the buoyant force on a submerged object is equal to the weight of the fluid displaced by the object. When a wooden cube is floating levelly in water, the weight of the water displaced is equal to the weight of the cube. Since the density of the cube is 700 kg/m³ and the density of water is 1000 kg/m³, the cube will float with a fraction of its volume submerged equal to the ratio of its density to that of water (700/1000).
The volume of the entire cube is 0.30 m * 0.30 m * 0.30 m = 0.027 m³. Therefore, the weight of the cube is its volume multiplied by its density, which is 0.027 m³ * 700 kg/m³ = 18.9 kg. Since only a fraction (0.7) of the cube will be submerged, to find the submerged volume we use the equation (submerged volume/total volume) = (cube's density/water's density). Solving for the submerged volume: 0.7 * 0.027 m³ = 0.0189 m³.
The height of the submerged portion of the cube can be found by dividing the submerged volume by the area of one face: 0.0189 m³ / (0.30 m * 0.30 m) = 0.21 m. Therefore, the distance from the top of the wood to the water surface is the total height of the cube minus the submerged height, which is 0.30 m - 0.21 m = 0.09 m.