Page:Calculus Made Easy.pdf/131

(10) A spherical balloon is increasing in volume. If, when its radius is $r$ feet, its volume is increasing at the rate of $4$ cubic feet per second, at what rate is its surface then increasing?

(11) Inscribe in a given sphere a cone whose volume is a maximum.

(12) The current $C$ given by a battery of $N$ similar voltaic cells is $C={\tfrac {n\times E}{R+{\frac {rn^{2}}{N}}}}$, where $E$, $R$, $r$, are constants and $n$ is the number of cells coupled in series. Find the proportion of $n$ to $N$ for which the current is greatest.