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.