# Balloon Problem

A punctured balloon, in the shape of a sphere, is losing air at the rate of
2 in.3/sec. At the moment that the balloon has volume 36π cubic inches,

I got

dr/dt = -1/18π in/sec.

Is that correct?

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HallsofIvy
Homework Helper
No, it is not. Had you shown your work, I could have helped you more.

Sorry about that Sir, here is what i did.

Volume = (4/3)$$\pi$$r3

dv/dt = -2 in3/sec

dv/dt = 4$$\pi$$r2dr/dt

I substituted 36$$\pi$$ into the volume equation to get the radius which is equal to 3

dr/dt = -2/(4$$\pi$$r2)

dr/dt = -1/(18$$\pi$$)

Could anyone spare the time to shed some light on this problem please. Thanks :)

Dick