To find the dimensions of a cube given its mass and density, you can use the formula for density:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
From this, you can rearrange the formula to find the volume (V):
\[ V = \frac{\text{Mass}}{\text{Density}} \]
In this case, the mass of the steel cube is 1,000 kg, and the density of steel is 8,000 kg/m³. Plugging in the values:
\[ V = \frac{1000 \text{ kg}}{8000 \text{ kg/m}^3} = 0.125 \text{ m}^3 \]
Since the cube's volume is also equal to \( \text{side}^3 \), we can find the length of one side (s) of the cube:
\[ s^3 = V \implies s = \sqrt[3]{V} \] \[ s = \sqrt[3]{0.125 \text{ m}^3} = 0.5 \text{ m} \]
The dimensions of the cube are \(0.5 , \text{m} \times 0.5 , \text{m} \times 0.5 , \text{m}\).
Thus, the correct response is:
0.5 m