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WAEC Further Mathematics 2014 Question 17

Question 17

Differentiation

The radius of a sphere is increasing at a rate of 3 cm s−1, find the rate of increase in the surface area, when the radius is 2cm.

  1. A.8π cm2s−1
  2. B.16π cm2s−1
  3. C.24π cm2s−1
  4. D.48π cm2s−1
Show the answer and explanation

Answer: D (48π cm2s−1)

Explanation

A = 4πr², dA/dt = 8πr × dr/dt = 8π(2)(3) = 48π cm²/s.