The density of the cube is approximately 618kg/m^3.
The change in the reading of the spring scale when the solid cube is submerged in water provides information about the buoyant force acting on the cube. The difference between the initial reading (5.40 N) and the submerged reading (3.38 N) represents the buoyant force, which is equal to the weight of the water displaced by the submerged cube. By applying Archimedes' principle, we can equate the buoyant force to the weight of the water displaced, allowing us to calculate the volume of the cube.
Once the volume is determined, we can use the formula for density (ρ= m/V), where m is the mass of the cube. Considering that weight is the product of mass and gravitational acceleration (W=mg), we can find the mass of the cube.
Finally, by substituting the mass and volume into the density formula, we calculate the density of the cube. The result, approximately 618kg/m^3, signifies the density of the material composing the cube. This approach utilizes principles of buoyancy, weight, and density to determine the cube's material density based on the observed changes in the spring scale readings.