Using the Definition to Compute the Derivative - Exercise 5

Exercise 5. A spherical balloon is being inflated. Find the rate at which its volume V is changing with respect to the radius.

Answer. The volume of the sphere is

$$V = \frac{4 \pi}{3} r^3\;.$$

So the desired rate of change is given by

$$\frac{dV}{dr} = 4 \pi r^2\;.$$

In particular, when r = 5 ft, the rate of change is

$${\frac{dV}{dr}}$$ = 100$$\pi$$  $${\frac{\mbox{ft}^3}{\mbox{sec}}}$$,

if time is measured in seconds.

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