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

1 answer

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