Verified Solution • 2025–26 Session moderate

QJEEM25Mad0b5: JEE Main 2025 Mathematics - Class 12 JEEM25Mad0b5 Solution: A spherical chocolate ball has a layer of ice-cream of uniform…

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 cm3/min81 \mathrm{~cm}^3 / \mathrm{min} and the thickness of the ice-cream layer decreases at the rate of 14π cm/min\frac{1}{4 \pi} \mathrm{~cm} / \mathrm{min} . The surface area (in cm2\mathrm{cm}^2 ) of the chocolate ball (without the ice-cream layer) is :

Multiple Choice Options

  • A 128π128 \pi
  • B 196π196 \pi
  • C 225π225 \pi
  • D 256π256 \pi

Step-by-Step Verified Solution

JEE Main 2025 (Online) 23rd January Evening Shift Mathematics - Application of Derivatives Question 4 English Explanation

v=43πr3dvdt=4πr2drdt81=4πr2×14πr2=81r=9 surface area of chocolate =4π(r−1)2=256π

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