Final answer:
To find the length of a side of a cube with a given mass and density, first calculate the volume by dividing the mass by the density. Then, take the cube root of the volume to find the length of one side of the cube.
Step-by-step explanation:
To find the length of a side of a cube with a given mass and density, we need to first calculate the volume of the cube. The volume of a cube can be found by cubing the length of one side. Using the formula for density, which is mass divided by volume, we can rearrange the formula to solve for volume: volume = mass / density. Once we have the volume, we can find the length of one side of the cube by taking the cube root of the volume.
Let's plug in the given values. The mass is 1.0 kg and the density is 2.3x1017 kg/m³. So, volume = 1.0 kg / (2.3x1017 kg/m³) = 4.34x10-18 m³. Taking the cube root of the volume gives us the length of one side of the cube: length = ∛(4.34x10-18 m³) = 1.57x10-6 m.