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MHT CET202310 May 2023Evening ShiftMathematicsApplication of DerivativesActual

If the surface area of a spherical balloon of radius 6 ~cm is increasing at the rate 2 ~cm ^2 / sec , then the rate of increase in its volume in cm ^3 / sec is

Options

  1. A16
  2. B6
  3. C12
  4. D8

Correct answer

B. 6

Step-by-step solution

Surface area, S=4 r^2 aligned & dS dt =8 r dr dt & 2=8 r dr dt & dr dt = 1 4 r ...(i) & Volume, V= 4 3 r^3 & dV dt = 4 3 3 r ^2 dr dt & =4 r^2 1 4 r ... [From (i)] & = r & =6 ~cm ^3 / sec & aligned

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