A spherical chocolate ball has a layer of ice-cream of uniform thickness around it

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

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 \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:

Related theory

Volume of Solids
Related Rates
Rates of change
Rate of change of quantities

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