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JEE Main2012MathematicsApplication of DerivativesActual

A spherical balloon is filled with 4500 ~ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72 ~ cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage began is

Options

  1. A9 7
  2. B7 9
  3. C2 9
  4. D9 2

Correct answer

C. 2 9

Step-by-step solution

v= 4 3 r^2 After 49 minutes volume =4500 -49(72 )=972 4 3 r^3=972 r^3=729 r=9v= 4 3 r^3 d v d t = 4 3 3 r^2 d r d t 72 =4 r^2 d r d t dr dt = 72 4 9 9 = 2 9

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