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KCET2023MathematicsApplication of Derivatives

A circular plate of radius 5 ~cm is heated. Due to expansion, its radius increase at the rate of 0.05 ~cm / s . The rate at which its area is increasing when the radius is 5.2 ~cm is

Options

  1. A27.4 cm ^2 / s
  2. B5.05 cm ^2 / s
  3. C0.52 cm ^2 / s
  4. D5.2 cm ^2 / s

Correct answer

C. 0.52 cm ^2 / s

Step-by-step solution

Let r be the radius of the circular disc and A be the area of the circular disc at any instant of time. we know that gathered A= r^2 d A d t =2 r d r d t gathered According to the question, the circular disc expands on heating with the rate of change of radius is 0.05 ~cm / s aligned d r d t & =0.05 ~cm / s d A d t & =2 5.2 0.05 d A d t & =0.52 cm ^2 / s aligned So, the rate at which its area is increasing, when radius is 5.2 ~cm is 0.52 cm ^2 / s .

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