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

[bobraymund]

Homework Statement

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

 

[Mark44]

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.

 

[HallsofIvy]

Homework Statement

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

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

 

[bobraymund]

Thanks guys!

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.

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