JEE Main 2025 — Application Of Derivatives Question with Solution

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 $81{\mathrm{cm}}^3/\min$ and the thickness of the ice-cream layer decreases at the rate of $\frac{1}{4\pi }\mathrm{cm}/\min$. The surface area (in ${\mathrm{cm}}^2$ ) of the chocolate ball (without the ice-cream layer) is :