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JEE Main2005MathematicsApplication of DerivativesActual

A spherical iron ball 10 ~cm in radius is coated with a layer of ice of uniform thickness than 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. B1 18 cm / min
  3. C1 54 cm / min
  4. D5 6 cm /

Correct answer

B. 1 18 cm / min

Step-by-step solution

aligned & d v d t =50 & 4 r^2 d r d t =50 & d r d t = 50 4 (15)^2 where r=15 & = 1 16 aligned

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