Posted by Mel on Monday, December 17, 2012 at 9:32pm.
A spherical party balloon is being inflated with helium pumped in at a rate of 12 cubic feet per minute. How fast is the radius growing at the instant when the radius has reached 1 ft?

mathcalculus  Reiny, Monday, December 17, 2012 at 9:45pm
V = (4/3)πr^3
dV/dt = 4π r^2 dr/dt
given : dV/dt = 12 , and r = 1
12 = 4π (1) dr/dt
dr/dt = 3/π ft/min

mathcalculus  Mel, Monday, December 17, 2012 at 10:40pm
Thank you! I initially thought the given rate of 12 cubic feet per minute was dr/dt.

mathcalculus  Reiny, Monday, December 17, 2012 at 11:15pm
The units are usually your giveaway.
it says 12 cubic feet/min which is volume/time , so dV/dt
This will work in most cases.

mathcalculus  12, Wednesday, March 23, 2016 at 12:13am
12
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