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MHT CET202120 Sep 2021Evening ShiftMathematicsApplication of DerivativesActual

The surface area of a spherical balloon is increasing at the rate 2 ~cm ^2 / sec . Then rate of increase in the volume of the balloon is , when the radius of the balloon is 6 ~cm .

Options

  1. A4 ~cm ^3 / sec
  2. B16 ~cm ^3 / sec
  3. C36 ~cm ^3 / sec
  4. D6 ~cm ^3 / sec

Correct answer

D. 6 ~cm ^3 / sec

Step-by-step solution

We have dA dt =2 and A =4 r ^2 aligned & dA dt =8 r dt dt 2=8 (6) dr dt & dr dt = 1 24 aligned Here V = 4 3 r ^3 aligned & dV dt =4 r ^2 dr dt & =4 (6)^2 ( 1 24 )=6 ~cm ^3 / sec aligned

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