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

Question

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...

Accepted Answer

$\begin{gathered} v=\frac{4}{3}\pi {r}^{3} \ \frac{dv}{dt}=4\pi {r}^{2}\frac{dr}{dt} \ 81=4\pi {r}^{2}	imes \frac{1}{4\pi } \ {r}^{2}=81 \ r=9 \ =4\pi (r-1{)}^{2}=256\pi \end{gathered}$

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