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

0.05 m
0.05 m

0.5 m
0.5 m

50 m
50 m

5 m

Answer 1

To find the dimensions of a cube given its mass and the density of the material, we can use the formula:

\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\]

First, we can rearrange this formula to solve for volume:

\[
\text{Volume} = \frac{\text{Mass}}{\text{Density}}
\]

Here, the mass of the steel cube is 1,000 kilograms, and the density is 8,000 kg/m³. Plugging in the values:

\[
\text{Volume} = \frac{1000 \text{ kg}}{8000 \text{ kg/m}^3} = 0.125 \text{ m}^3
\]

The volume \(V\) of a cube is also given by \(V = s^3\), where \(s\) is the length of a side of the cube. So, we can set up the equation:

\[
s^3 = 0.125 \text{ m}^3
\]

To find \(s\), we take the cube root:

\[
s = \sqrt[3]{0.125} = 0.5 \text{ m}
\]

Therefore, the dimensions of the cube are \(0.5 \text{ m} \times 0.5 \text{ m} \times 0.5 \text{ m}\).

So the correct response is:

**0.5 m**