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WAEC Further Mathematics 2013 Question 24

Question 24

Differentiation

A circular ink blot on a piece of paper increases its area at the rate of 4 mm2/s. Find the rate of increase of the radius of the blot when the radius is 8 mm. [Take π = 22/7].

  1. A.0.25 mm/s
  2. B.0.20 mm/s
  3. C.0.08 mm/s
  4. D.0.05 mm/s
Show the answer and explanation

Answer: C (0.08 mm/s)

Explanation

dA/dt = 2πr × dr/dt, so dr/dt = 4/(2 × 22/7 × 8) = 7/88 ≈ 0.08 mm/s.