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JAMB Mathematics 2000 Question 38

Question 38

Differentiation

If the volume of a hemisphere is increasing at a steady rate of 18πm3s−1, at what rate is its radius changing when it is 6m?

  1. A.2.50ms−1
  2. B.2.00ms−1
  3. C.0.25ms−1
  4. D.0.20ms−1
Show the answer and explanation

Answer: C (0.25ms−1)

Explanation

V = (2/3)πr3, so dV/dt = 2πr2 × dr/dt. With r = 6: 18π = 72π × dr/dt, so dr/dt = 0.25 m/s.