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

5 m
5 m

0.05 m
0.05 m

0.5 m

Answer 1

To find the dimensions of the cube, we can use the formula for density:

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

From the problem, we know:
- Mass = 1,000 kg
- Density = 8,000 kg/m³

First, we can rearrange the density formula to find the volume:

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

Next, since the shape of the object is a cube, we use the formula for the volume of a cube, which is:

\[
\text{Volume} = s^3
\]

Where \(s\) is the length of one side of the cube. We can set the two equations for volume equal to each other:

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

Now, we take the cube root of both sides to find \(s\):

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

So, the dimensions of the cube are **0.5 m**.