# Express dV/dt in terms of dr/dt - Derivative Word Problem

1. Oct 13, 2009

### bobraymund

1. The problem statement, all variables and given/known data

Air is being pumped into a spherical weather balloon. At any time t, the volume of the balloon is V(t) and its radius is r(t).

Express dV/dt in terms of dr/dt.

2. The attempt at a solution

Volume of a Sphere = 4/3 pi r3

I took the derivative of the formula above and got:

I ended up getting:

Did I do this completely wrong? If so, what am I supposed to do?

Thanks,
Bob

#### Attached Files:

• ###### 3pir2_fracdrdt.gif
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2. Oct 13, 2009

### Staff: Mentor

You're right on the money.

In LaTeX script, your equation looks like this:
$$\frac{dV}{dt}~=~4\pi r^2 \frac{dr}{dt}$$

To see the script, click on the expression, and another browser window opens with the LaTeX script.

3. Oct 13, 2009

### HallsofIvy

Staff Emeritus
I don't see anything at all wrong with it!

4. Oct 13, 2009

### bobraymund

Thanks guys!

Oh, thanks. I've been using a site called Texify to generate all these pictures! This will save a lot of my time in the future.

Thanks again,
Bob