To find the dimensions of the cube, you can use the formula for density, which is:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
The volume of a cube can be expressed as \( V = s^3 \), where \( s \) is the length of one side of the cube.
Given:
- Mass of the cube (m) = 1000 kg
- Density of steel (ρ) = 8000 kg/m³
First, we can rearrange the density formula to find the volume:
\[ V = \frac{m}{\rho} = \frac{1000 , \text{kg}}{8000 , \text{kg/m}^3} = 0.125 , \text{m}^3 \]
Now, we can find the length of one side of the cube \( s \):
\[ s^3 = V = 0.125 , \text{m}^3 \]
To find \( s \), take the cube root of the volume:
\[ s = \sqrt[3]{0.125} = 0.5 , \text{m} \]
Thus, the dimensions of the cube are \( 0.5 , \text{m} \) for each side.
Therefore, the correct response is:
0.5 m