JAMB 2012 Mathematics · Question 40

U is inversely proportional to the cube of V and U = 81 when V = 2. Find U when V = 3

Options

A.24
B.27
C.32
D.36

Answer: A. 24

Explanation written with AI and checked against the answer key

Analyze the question: U is inversely proportional to V³. We're given one pair of values (U = 81, V = 2) and asked to find U when V = 3. Concept: Inverse proportion to the cube means U = k/V³, where k is a constant. Solution: Step 1: Find k using U = 81 when V = 2. 81 = k/2³ = k/8 k = 81 × 8 = 648 Step 2: Use k to find U when V = 3. U = 648/3³ = 648/27 = 24 Check with the ratio method: U₁V₁³ = U₂V₂³ 81 × 8 = U₂ × 27 U₂ = 648/27 = 24 ✓ Tip: For "inversely proportional to the cube", always write U = k/V³ and find k first. You can also use the shortcut U₁V₁³ = U₂V₂³ to skip finding k. Also check your answer: V increased from 2 to 3, so U must decrease, and 24 < 81 fits.

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