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MHT CET20226 Aug 2022Evening ShiftMathematicsApplication of DerivativesActual

A spherical iron ball of 10 ~cm radius is coated with a layer of ice of uniform thickness that melts at the rate of 50 ~cm ^3 / min . If the thickness of ice is 5 ~cm , then the rate at which the thickness of ice decrease is

Options

  1. A1 18 cm / min
  2. B2 9 cm / min
  3. C-1 18 cm / min
  4. D1 3 cm / min

Correct answer

A. 1 18 cm / min

Step-by-step solution

aligned & v= 4 3 r^3 & d v d t =50 r=(10+5)=15 ~cm & d v d t =4 r^2 d r d t & 50=4 15 15 d r d t & d r d t = 50 4 15 15 = 1 18 cm / min aligned

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