# [SOLVED] rate problem

• October 11th 2007, 02:23 PM
jst706
[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
• October 11th 2007, 03:03 PM
galactus
They give you dV/dt=25 and r=2.

We need dr/dt when r=2

Differentiate the sphere volume formula:

$4{\pi}r^{2}\frac{dr}{dt}=25$

Now, plug in r=2 and solve for dr/dt