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
?(1 point)
Responses
5 m
5 m
0.5 m
0.5 m
50 m
50 m
0.05 m
Answers
GPT-4o mini
To find the dimensions of the cube, we first need to calculate the volume using the mass and density of the steel.
The formula for density (\( \rho \)) is:
\[
\rho = \frac{mass}{volume}
\]
Rearranging this formula to find the volume (\( V \)) gives us:
\[
V = \frac{mass}{\rho}
\]
Substituting in the values:
\[
V = \frac{1000 \text{ kg}}{8000 \text{ kg/m}^3} = 0.125 \text{ m}^3
\]
Now, since the volume of a cube (\( V \)) can also be expressed as:
\[
V = s^3
\]
where \( s \) is the length of one side of the cube, we can find \( s \) by taking the cube root of the volume:
\[
s = \sqrt[3]{V} = \sqrt[3]{0.125} \approx 0.5 \text{ m}
\]
Thus, the dimensions of the cube are approximately **0.5 meters** on each side. The correct response is:
**0.5 m**
The formula for density (\( \rho \)) is:
\[
\rho = \frac{mass}{volume}
\]
Rearranging this formula to find the volume (\( V \)) gives us:
\[
V = \frac{mass}{\rho}
\]
Substituting in the values:
\[
V = \frac{1000 \text{ kg}}{8000 \text{ kg/m}^3} = 0.125 \text{ m}^3
\]
Now, since the volume of a cube (\( V \)) can also be expressed as:
\[
V = s^3
\]
where \( s \) is the length of one side of the cube, we can find \( s \) by taking the cube root of the volume:
\[
s = \sqrt[3]{V} = \sqrt[3]{0.125} \approx 0.5 \text{ m}
\]
Thus, the dimensions of the cube are approximately **0.5 meters** on each side. The correct response is:
**0.5 m**