Question

pumping 1 𝑑mˆ3 air per second into a balloon. How fast increasing radius when the diameter is 20 𝑐𝑚?

Answer 1

well the volume of the balloon is

\[V = \frac{4}{3} \pi r^3\]

so find \[\frac{dV}{dr}\]

when you find the derivative, then find the reciprocal

you will need

\[\frac{dr}{dV} \]

later

you are given \[\frac{dV}{dt} = 1\]

and you need to find

\[\frac{dr}{dt}\]

so you can use the chain rule

\[\frac{dr}{dt} = \frac{dr}{dV} \times \frac{dV}{dt}\]

hope it makes sense

Answer 2

when you get

\[\frac{dr}{dt}\]

when the diameter is 20, the radius is 10, so substitute r = 10 and evaluate