Related Rate HELP

Quote:

Originally Posted by claybird

I have about 20 related rate problems that I just cannot get a grasp on. (Headbang) I'll post a couple, and anyone who can show me how to work them would be greatly appreciated. I think if I can see a couple worked out, I can get the rest of them alright.

2. A sphirical balloon is inflated at a rate of 16 cubic feet per minute. How fast is the radius of the balloon changing at the instant the radius is 2 feet?

Thanks for all the help; for some reason this stuff just doesn't click.:confused:

Recall that the volume of the sphere is defined as $V=\tfrac{4}{3}\pi r^3$ .

We are given $\frac{\,dV}{\,dt}=16\frac{ft^3}{s}$

We want to find $\frac{\,dr}{\,dt}$ when $r=2~ft$ .

Thus, we should differentiate the volume equation:

$V=\tfrac{4}{3}\pi r^3\implies \frac{\,dV}{\,dt}=4\pi r^2\frac{\,dr}{\,dt}$

We know $\frac{\,dV}{\,dt}$ and $r$ . Now it should be easy to find $\frac{\,dr}{\,dt}$ :D

--Chris