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MHT CET202210 Aug 2022Morning ShiftMathematicsApplication of DerivativesActual

A spherical iron ball 10 ~cm in 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 at which the thickness of ice decreases, is

Options

  1. A1 36 cm / min
  2. B5 6 cm / min
  3. C1 54 cm / min
  4. D1 18 cm / min

Correct answer

D. 1 18 cm / min

Step-by-step solution

aligned & V= 4 3 r^3 & d v ~d t =4 r^2 d r ~d t & 50=4 15^2 d r ~d t & d r ~d t = 50 4 15^2 = 1 18 cm / min aligned

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