# Homework Help: Balloon Problem

1. Jun 13, 2010

### Brandon_R

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?

2. Jun 13, 2010

### HallsofIvy

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

3. Jun 13, 2010

### Brandon_R

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$$\pi$$)

4. Jun 16, 2010

### Brandon_R

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

5. Jun 16, 2010

### Dick

That looks fine to me. Halls may have called it wrong since you wrote -1/18 pi instead of -1/(18 pi).

6. Jun 16, 2010

### HallsofIvy

Ah, thanks, Dick!