
[SOLVED] rate problem
A spherical balloon is being inflated at a constant rate of 25cm/sec. At what rate in cm/sec is the radius of the balloon changing when the radius is 2cm?
I have the volume which is 4/3*(pi)*8.
I thought the answer would be 25 divided by the volume, but I guess I was wrong because the answer key says 25/16pi?
How would I go about setting this problem up? thanks

They give you dV/dt=25 and r=2.
We need dr/dt when r=2
Differentiate the sphere volume formula:
$\displaystyle 4{\pi}r^{2}\frac{dr}{dt}=25$
Now, plug in r=2 and solve for dr/dt