Final answer:
To find the length of a cube with a given mass and density, we can use the formula: density = mass/volume. Rearrange the formula to solve for the volume, substitute the values, and then find the cube root of the volume to get the side length. The length of a side of the cube is approximately 1.60×10⁻⁶ meters.
Step-by-step explanation:
To find the length of a side of a cube given the mass and density, we can use the formula:
density = mass/volume
Since the density is given as 2.3×10¹⁷ kg/m³ and the mass is 1.0 kg, we can rearrange the formula to solve for the volume:
volume = mass/density
Substituting the values, we have:
volume = 1.0 kg / 2.3×10¹⁷ kg/m³ = 4.35×10⁻¹⁷ m³
A cube has all sides equal, so the volume of the cube is given by:
volume of cube = (side length)³
Substituting the volume we found, we have:
(side length)³ = 4.35×10⁻¹⁷ m³
Taking the cube root of both sides, we can solve for the side length:
side length = ∛(4.35×10⁻¹⁷ m³) ≈ 1.60×10⁻⁶ m
Therefore, the length of a side of the cube is approximately 1.60×10⁻⁶ meters.