To find the dimensions of the cube, we need to use the formula for density:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
Given that the mass of the cube is 1,000 kg and the density of steel is 8,000 kg/m³, we can rearrange the formula to find the volume:
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{1000 , \text{kg}}{8000 , \text{kg/m}^3} = 0.125 , \text{m}^3 \]
Next, since the volume \( V \) of a cube is given by \( V = a^3 \) where \( a \) is the length of a side of the cube, we can solve for \( a \):
\[ a^3 = 0.125 , \text{m}^3 \]
Taking the cube root of both sides:
\[ a = \sqrt[3]{0.125} = 0.5 , \text{m} \]
Thus, the dimensions of the cube are 0.5 m.
So, the correct response is:
- 0.5 m