Solve Rate of Change for Spherical Balloon Radius: 500 cc/min

[bjr_jyd15]

Hi everyone. I'm stuck on this problem in calc:

A spherical balloon is inflated with gas at the rate of 500 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is a)30 cm and b)60 cm?

Here's what I have so far.

V=4/3*pi r^3

dV/dt=500

dr/dt=?

dV/dt=4/3*pi (3r^2) dr/dt

Where can I go from here? Any help would be great. Thanks

 

[arildno]

OOPS, MAJOR EDIT:
"dV/dt=4/3*pi (3r^2) dr/dt"
You've got this equation, right?
So, regrouping you have:
$$\frac{dr}{dt}=\frac{1}{4{\pi}r^{2}}\frac{dV}{dt}$$

 

[bjr_jyd15]

got it

thanks, i got it. The 4/3 just screwed me up. i just plugged dv/dt from original info.