To find the dimensions of the cube, we can use the formula for density:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
First, we need to calculate the volume of the steel cube using its mass and density. Rearranging the formula gives us:
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]
Given:
- Mass = 1,000 kg
- Density = 8,000 kg/m³
Now, substituting the values into the equation:
\[ \text{Volume} = \frac{1000 , \text{kg}}{8000 , \text{kg/m}^3} = 0.125 , \text{m}^3 \]
Next, since the cube's volume can also be calculated as \( \text{Volume} = s^3 \) (where \( s \) is the length of one side of the cube), we set the two equations equal to each other:
\[ s^3 = 0.125 \]
Taking the cube root:
\[ s = \sqrt[3]{0.125} \]
Calculating that gives:
\[ s = 0.5 , \text{m} \]
Thus, the dimensions of the cube are \( 0.5 , \text{m} \times 0.5 , \text{m} \times 0.5 , \text{m} \).
The correct response is:
0.5 m 0.5 m 0.5 m