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AP EAMCET201823 Apr 2018Evening ShiftMathematicsApplication of DerivativesActual

Air is discharging from a large spherical balloon at the rate of 4 cubic meters per minute. Then, the rate at which the surface area is shrinking when the radius of the balloon is 8 ~m , is

Options

  1. A2 ~m ^2 / min
  2. B1 ~m ^2 / min
  3. C4 ~m ^2 / min
  4. D8 ~m ^2 / min

Correct answer

B. 1 ~m ^2 / min

Step-by-step solution

Let air is discharging from a large spherical balloon, at the rate d v d t =4 ~m ^3 / min V= 4 3 r^3 , where r is the radius of spherical balloon. So, aligned & So, aligned d v d t & =4 r^2 d r d t at r=8 ~m 4 & =4 (64) d r d t d r d t = 1 64 m / min Area s=4 r^2 & d s d t =4 (2 r) d r d t at r=8 ~m d s d t & =64 1 64 =1 ~m ^2 / min . aligned aligned

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