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UI Post-UTME Mathematics 2023 (Model questions) Question 17

Question 17

Differentiation

The radius of a circle is increasing at a rate of 2cm/s. What is the rate of change of the area of the circle when the radius is 5cm?

  1. A.4πcm2/s
  2. B.20πcm2/s
  3. C.25πcm2/s
  4. D.16πcm2/s
Show the answer and explanation

Answer: B (20πcm2/s)

Explanation

dA/dt = 2πr × dr/dt = 2π(5)(2) = 20π cm²/s.