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BITSAT2024MathematicsApplication of DerivativesActual

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

Options

  1. A30 ~cm / sec
  2. B160 3 ~cm / sec
  3. C10 ~cm / sec
  4. D160 ~cm / sec

Correct answer

B. 160 3 ~cm / sec

Step-by-step solution

Let be the semi-vertical angle and r be the radius of the cone at time t . the radius of the cone at time t . Then, r=20 d r d t =20 ^2 d d t d r d t =20 ^2 30^ 2 [ =30^ . and . d d t =2 ] d r d t =20 4 3 2 ~cm / s = 160 3 ~cm / s

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