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
50 m
50 m
0.05 m
0.05 m
0.5 m
Responses
5 m
5 m
50 m
50 m
0.05 m
0.05 m
0.5 m
Answers
GPT-4o mini
To find the dimensions of the cube, we need to use the formula for density:
\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\]
Given that the mass of the cube is 1,000 kg and the density of steel is 8,000 kg/m³, we can rearrange the 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 volume \( V \) of a cube is given by \( V = a^3 \) where \( a \) is the length of a side of the cube, we can solve for \( a \):
\[
a^3 = 0.125 \, \text{m}^3
\]
Taking the cube root of both sides:
\[
a = \sqrt[3]{0.125} = 0.5 \, \text{m}
\]
Thus, the dimensions of the cube are **0.5 m**.
So, the correct response is:
- **0.5 m**
\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\]
Given that the mass of the cube is 1,000 kg and the density of steel is 8,000 kg/m³, we can rearrange the 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 volume \( V \) of a cube is given by \( V = a^3 \) where \( a \) is the length of a side of the cube, we can solve for \( a \):
\[
a^3 = 0.125 \, \text{m}^3
\]
Taking the cube root of both sides:
\[
a = \sqrt[3]{0.125} = 0.5 \, \text{m}
\]
Thus, the dimensions of the cube are **0.5 m**.
So, the correct response is:
- **0.5 m**