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Manipal MET2018MathematicsApplication of Derivatives

If the rate of change in the circumference of a circle of 0.3 ~cm / s , then the rate of change in the area of the circle when the radius is 5 cm , is

Options

  1. A1.5 sq cm / s
  2. B0.5 sq cm / s
  3. C5 sq cm / s
  4. D3 sq cm / s

Correct answer

A. 1.5 sq cm / s

Step-by-step solution

Circumference of circle, C=2 r aligned & d C d t =2 d r d t & 0.3 2 = d r d t aligned ( d C d t =0.3 ~cm / s given ) 1 Now, A= r^2 array cc & d A d t =2 r d r d t d A d t =r 0.3 & [ d A d t ]_ r=5 =5 0.3=1.5 sq ~cm / s array

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