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?

- math-calculus -
**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

- math-calculus -
**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.

- math-calculus -
**Reiny**, Monday, December 17, 2012 at 11:15pm
The units are usually your give-away.

it says 12 cubic feet/min which is volume/time , so dV/dt

This will work in most cases.

- math-calculus -
**12**, Wednesday, March 23, 2016 at 12:13am
12

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