Question

The density of a 200 g gabbro sample, cut in the form of a cube, is 3125 kg/m³. The length of the sample is ________ mm. (Answer in integer.)

Hint:

To find cube edge: \( l = \sqrt[3]{\frac{m}{\rho}} \). Convert units before solving.

Answer 1

Correct Answer: 40

Step 1: Formula used.
Density (\( \rho \)) = Mass / Volume.
Volume = \( \dfrac{\text{Mass}}{\text{Density}} \).
Step 2: Substitution.
Mass = 200 g = 0.2 kg, \( \rho = 3125 \, \text{kg/m}^3 \).
\[ V = \frac{0.2}{3125} = 6.4 \times 10^{-5} \, \text{m}^3 \] Step 3: Cube length.
\[ l = V^{1/3} = (6.4 \times 10^{-5})^{1/3} = 0.04 \, \text{m} = 40 \, \text{mm} \] Step 4: Conclusion.
The cube’s edge length = 40 mm.