Question

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
50 m

0.05 m
0.05 m

Answer 1

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**