Question

A cube of edge 4 cm has mass 256 g. The density of the material in SI unit is:

• A. \( 4 \, \text{kg/m}^3 \)
• B. \( 1600 \, \text{kg/m}^3 \)
• C. \( 4000 \, \text{kg/m}^3 \)
• D. \( 1000 \, \text{kg/m}^3 \)

Hint:

Always convert cm to m and grams to kilograms when using SI units. Volume of cube is \( a^3 \), and density is mass divided by volume.

Answer 1

The Correct Option is B

Given: - Edge of cube \( a = 4 \, \text{cm} = 0.04 \, \text{m} \) - Mass \( m = 256 \, \text{g} = 0.256 \, \text{kg} \) Volume of cube: \[ V = a^3 = (0.04)^3 = 6.4 \times 10^{-5} \, \text{m}^3 \] Density \( \rho = \frac{m}{V} = \frac{0.256}{6.4 \times 10^{-5}} = 4000 \, \text{kg/m}^3 \) Oops! This contradicts the correct answer given. Actually, correcting the math: \[ (0.04)^3 = 0.000064 = 6.4 \times 10^{-5} \] \[ \rho = \frac{0.256}{6.4 \times 10^{-5}} = 4000 \, \text{kg/m}^3 \] So the correct answer should be: Correct Answer: (3) \( \boxed{4000 \, \text{kg/m}^3} \)