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
0.5 m
0.5 m
5 m
5 m
0.05 m
0.05 m
50 m
Responses
0.5 m
0.5 m
5 m
5 m
0.05 m
0.05 m
50 m
Answers
GPT-4o mini
To find the dimensions of a cube given its mass and density, you can use the formula for density:
\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\]
From this, you can rearrange the formula to find the volume (V):
\[
V = \frac{\text{Mass}}{\text{Density}}
\]
In this case, the mass of the steel cube is 1,000 kg, and the density of steel is 8,000 kg/m³. Plugging in the values:
\[
V = \frac{1000 \text{ kg}}{8000 \text{ kg/m}^3} = 0.125 \text{ m}^3
\]
Since the cube's volume is also equal to \( \text{side}^3 \), we can find the length of one side (s) of the cube:
\[
s^3 = V \implies s = \sqrt[3]{V}
\]
\[
s = \sqrt[3]{0.125 \text{ m}^3} = 0.5 \text{ m}
\]
The dimensions of the cube are \(0.5 \, \text{m} \times 0.5 \, \text{m} \times 0.5 \, \text{m}\).
Thus, the correct response is:
**0.5 m**
\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\]
From this, you can rearrange the formula to find the volume (V):
\[
V = \frac{\text{Mass}}{\text{Density}}
\]
In this case, the mass of the steel cube is 1,000 kg, and the density of steel is 8,000 kg/m³. Plugging in the values:
\[
V = \frac{1000 \text{ kg}}{8000 \text{ kg/m}^3} = 0.125 \text{ m}^3
\]
Since the cube's volume is also equal to \( \text{side}^3 \), we can find the length of one side (s) of the cube:
\[
s^3 = V \implies s = \sqrt[3]{V}
\]
\[
s = \sqrt[3]{0.125 \text{ m}^3} = 0.5 \text{ m}
\]
The dimensions of the cube are \(0.5 \, \text{m} \times 0.5 \, \text{m} \times 0.5 \, \text{m}\).
Thus, the correct response is:
**0.5 m**