JAMB 2013 Physics · Question 11

What volume of alcohol will have same mass as 4.2m-3 of petrol? Density of alcohol = 8.4 x 10^2 kgm-3, density of petrol =7.2x10^2 kgm-3

Options

A.0.8m3
B.1.4m3
C.3.6m3
D.49.m3

Answer: C. 3.6m3

Explanation written with AI and checked against the answer key

Analyze the question: We need the volume of alcohol whose mass equals the mass of 4.2 m³ of petrol. Concept: Mass = density × volume (m = ρV). If the masses are equal: ρ_alcohol × V_alcohol = ρ_petrol × V_petrol Solution: Mass of petrol = 7.2 × 10² × 4.2 = 720 × 4.2 = 3024 kg Volume of alcohol = mass ÷ density = 3024 ÷ 840 = 3.6 m³ Check by formula: V_alcohol = (7.2 × 10² × 4.2) / (8.4 × 10²) = (7.2 × 4.2) / 8.4 = 7.2 × 0.5 = 3.6 m³ Answer: 3.6 m³, which is option C. Sense check: Alcohol is denser than petrol here (840 vs 720 kg/m³), so a smaller volume of alcohol is needed to match the same mass. 3.6 m³ is less than 4.2 m³, which fits. Tip: When masses are equal, density and volume are inversely proportional: ρ₁V₁ = ρ₂V₂. The denser liquid always needs the smaller volume, so you can quickly eliminate options larger than 4.2 m³ (like D) in this question.

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