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JEE Main20209 Jan 2020Morning ShiftMathematicsApplication of DerivativesActual

A spherical iron ball of 10 c m radius is coated with a layer of ice of uniform thickness that melts at a rate of 50 c m 3 / m i n . When the thickness of ice is 5 c m , then the rate (in c m / m i n .) 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

Let thickness = x   cm Total volume V = 4 3 π 10 + x 3 d V d t = 4 π 10 + x 2 d x d t … . . ( i ) Given d V d t = 50   cm 3 / min At x = 5   cm 50 = 4 π 10 + 5 2 d x d t d x d t = 1 18 π   cm / min

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