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COMEDK2023Evening ShiftMathematicsApplication of DerivativesActual

The altitude of a cone is 20 cm and its semi vertical angle is 30^ . If the semi vertical angle is increasing at the rate of 2 radians per second, then the radius of the base is increasing at the rate of

Options

  1. A160 3 ~cm / sec
  2. B10 ~cm / sec
  3. C30 ~cm / sec
  4. D160 ~cm / sec

Correct answer

A. 160 3 ~cm / sec

Step-by-step solution

r = h Differentiating w.r.t. time ( h is constant): dr dt = h ^2 d dt At = 30° : ^2 30° = 4 3 , h = 20 cm, d dt = 2 rad/sec dr dt = 20 4 3 2 = 160 3 cm/sec

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