Related rates Balloon question. Thanks

[nukeman]

Homework Statement

Air is being pumped into a spherical balloon. Suppose we know the surface area of the balloon increases at a rate of 20cm^2/s when its radius is 4cm. What is the rate its volume is changing at that instant?

Homework Equations

The Attempt at a Solution

I went...

dv/dt = 4∏ (4)^2 * 20/1 = 1280∏

I know its wrong. Anyone help me out? What am i doing wrong?

 

[nukeman]

Wait no, I went:

dv/dt = (1/4pi(4)^2) *20/1

gives me 5 / 16pi

 

[haruspex]

I think that's still wrong. Write out generic formulae for dV/dt and dA/dt as functions of r and dr/dt..