A cube of steel has a mass of 1,000 kilograms. What are the dimensions of the cube if the density of steel is 8,000 kg/m3 ?(1 point) Responses 5 m 5 m 0.5 m 0.5 m 50 m

1 answer

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