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MHT CET202210 Aug 2022Evening ShiftMathematicsApplication of DerivativesActual

The radius of a cylinder is increasing at the rate 2 ~cm / sec and its height is decreasing at the rate of 3 ~cm / sec , then the rate of change of volume, when radius is 3 ~cm and the height is 5 ~cm , is

Options

  1. A44 cm ^3 / sec
  2. B11 cm ^3 / sec
  3. C23 cm ^3 / sec
  4. D33 cm ^3 / sec

Correct answer

D. 33 cm ^3 / sec

Step-by-step solution

V= r^2 h aligned & d v ~d t = (2 r d r ~d t h+r^2 d h ~d t ) & d v ~d t = (2 3 2 5+3^2 (-3) ) & d v ~d t =33 cm ^3 / sec aligned

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