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MHT CET20243 May 2024Morning ShiftMathematicsApplication of DerivativesActual

A stone is dropped into a quiet lake and waves move in circles at speed of 8 ~cm / sec . At the instant when the radius of the circular wave is 12 cm . how fast is the enclosed area increasing?

Options

  1. A180 ~cm ^2 / sec
  2. B196 ~cm ^2 / sec
  3. C192 ~cm ^2 / sec
  4. D200 ~cm ^2 / sec

Correct answer

C. 192 ~cm ^2 / sec

Step-by-step solution

Given, the rate of increasing the radius aligned & = dr dt =8 ~cm / sec & Area =A= r^2 & dA dt =2 dr & dA dt =2 (12)(8) & [ r =12 ~cm ] & =192 ~cm ^2 / sec aligned

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