Find the volume of a sphere with respect to time

[bobsmith76]

Homework Statement

I guess I should point out that the volume was known, which is 100 cm.

The Attempt at a Solution

I don't see why using the chain rule compels you to take the inverse of 4∏r^2. Any help would be appreciated.

I have a feeling that the solution is something like

100 = (4pir^2)/x

but that still is not right.

 

[SammyS]

I don't see why using the chain rule compels you to take the inverse of 4∏r^2. Any help would be appreciated.

They're simply solving $\displaystyle \frac{dV}{dt}=4\pi r^2\frac{dr}{dt}\ \text{ for }\ \frac{dr}{dt}\,.$

 

[bobsmith76]

Ok, now I got it. The way the book proceeded was a bit bewildering. I didn't see how dV/dt = 100, and r = 25, but now I do.