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

50 m
50 m

0.5 m
0.5 m

0.05 m
0.05 m

5 m
5 m

Answer 1

To find the dimensions of the cube, we can use the following formulas:

1. **Density Formula**:
\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\]
Rearranging this gives:
\[
\text{Volume} = \frac{\text{Mass}}{\text{Density}}
\]

2. **Volume of a Cube**:
\[
\text{Volume} = \text{side}^3
\]

Given that the mass of the steel cube is \( 1000 \) kg and the density of steel is \( 8000 \) kg/m³, we can calculate the volume:

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

Next, we can find the side length of the cube:

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

Thus, the dimensions of the cube are \( 0.5 \) m.

The correct response is:
**0.5 m**.