A solid cube of aluminum is 1.5cm on each edge. The density of aluminum is 2700kgm$^{-1}$. Find the mass of the cube.

Analyze the question: We need the mass of an aluminum cube with edge 1.5 cm, given its density. (The density unit should be kg m⁻³, not kg m⁻¹. This is a typo in the question, since density is mass per unit volume.)

Concept: Density = mass ÷ volume, so Mass = density × volume

Solution:

1. Volume of the cube: V = (1.5 cm)³ = 3.375 cm³

2. Convert the density to g/cm³: 2700 kg/m³ = 2700 × 1000 g ÷ 10⁶ cm³ = 2.7 g/cm³

3. Mass: m = 2.7 × 3.375 = 9.1125 g ≈ 9.1 g

Check in SI units: V = (0.015 m)³ = 3.375 × 10⁻⁶ m³ m = 2700 × 3.375 × 10⁻⁶ = 9.1125 × 10⁻³ kg = 9.1 g

Answer: The mass is about 9.1 g, which is option B.

Tip: Remember that 1 g/cm³ = 1000 kg/m³. So any density in kg/m³ can be divided by 1000 to get g/cm³ quickly (2700 → 2.7). Then multiply by the volume in cm³ and you get the mass in grams directly.