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AP EAMCET202120 Aug 2021Evening ShiftMathematicsApplication of DerivativesActual

A spherical iron ball of 10 cm radius is coated with a layer of ice of uniform thickness that melts at a rate of 50 cm 3 / min . When the thickness of ice is 5 cm , then the rate (in cm / min . ) at which of the thickness of ice decreases, is

Options

  1. A5 6 π
  2. B1 54 π
  3. C1 36 π
  4. D1 18 π

Correct answer

D. 1 18 π

Step-by-step solution

We know that, the volume of a sphere of radius r is 4 3 πr 3   c m 3 . It is given that, a spherical iron ball of 10   cm radius is coated with a layer of ice of uniform thickness, let the thickness is ' x ' cm , then volume of the ball is V = 4 3 π 10 + x 3   c m 3 . On differentiating w.r.t. ' t ', we get d V d t = 4 π 10 + x 2 d x d t . . . ( i ) where t is time in min . It is given, the d V d t = - 50   cm 3 / min , when x is 5   cm , then - 50 = 4 π

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