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BITSAT2022MathematicsApplication 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 ~min after the leakage began is

Options

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

Correct answer

C. 2 9

Step-by-step solution

V= 4 3 r^3 4500 = 4 r^3 3 r=15 ~m After 49 =(4500-49.72) =972 m ^3 aligned & & 972 & = 4 3 r^3 & & r^3 & =3 243=3 3^5 aligned aligned r & =9 d v d t & =4 r^2 ( d r d t ) 72 & =4 9 9 ( d r d t ) d r d t & = ( 2 9 ) aligned

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