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 / min and the thickness of the ice-cream layer decreases at the rate of 1/(4π) cm / min. The surface area (in cm²) of the chocolate ball (without the ice-cream layer) is:

Limit, Continuity and Differentiability: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q238

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumLimit, Continuity and Differentiability420× since 2002

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 \, \text{cm}

, the ice-cream melts at the rate of

81 \, \text{cm}^3 / \text{min}

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

\frac{1}{4\pi} \, \text{cm} / \text{min}

. The surface area (in

\text{cm}^2

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

JEE Main 2025 Limit, Continuity and Differentiability Question with Solution (January Unspecified (session-level dataset), Q238) | JEE Arc