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JEE Main202523 Jan 2025Evening ShiftMathematicsApplication of DerivativesActual

A spherical chocolate ball has a layer of ice-cream of uniform thickness around it. When the thickness of the ice-cream layer is 1 cm , the ice-cream melts at the rate of 81 ~cm ^3 / min and the thickness of the ice-cream layer decreases at the rate of 1 4 ~cm / min . The surface area (in cm ^2 ) of the chocolate ball (without the ice-cream layer) is :

Options

  1. A196
  2. B256
  3. C225
  4. D128

Correct answer

B. 256

Step-by-step solution

aligned & v = 4 3 r ^3 & dv dt =4 r ^2 dr dt & 81=4 r ^2 1 4 & r ^2=81 & r =9 aligned surface area of chocolate =4 (r-1)^2=256

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