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WAEC Further Mathematics 2011 Question 20

Question 20

Differentiation

What percentage increase in the radius of a sphere will cause its volume to increase by 45%?

  1. A.10%
  2. B.15%
  3. C.20%
  4. D.25%
Show the answer and explanation

Answer: B (15%)

Explanation

V = (4/3)πr3, so for small changes δV/V ≈ 3 δr/r. Then 45% = 3 × (δr/r), giving about 15%.