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Application of Derivatives question

2025 · 23 Jan · Shift 2 · Q43

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JEE Main
Mathematics
Application of Derivatives
2025 · 23 Jan · Shift 2 · Q43

Application of Derivatives question

2025 · 23 Jan · Shift 2 · Q43

JEE MainMathematicsApplication of DerivativesMCQ+4 / −1

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 \mathrm{~cm}^3 / \mathrm{min}

and the thickness of the ice-cream layer decreases at the rate of

\frac{1}{4 \pi} \mathrm{~cm} / \mathrm{min}

. The surface area (in

\mathrm{cm}^2

) of the chocolate ball (without the ice-cream layer) is :

A
$128 \pi$
B
$196 \pi$
C
$225 \pi$
D
$256 \pi$

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