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

Question

campbell_st · Answer

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

campbell_st · Answer

when you get 

$$\frac{dr}{dt}$$

when the diameter is 20, the radius is 10, so substitute r = 10 and evaluate