1. ## Related Rate HELP

I have about 20 related rate problems that I just cannot get a grasp on. 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.

1. A machine is rolling a metal cylinder under pressure. The radius of the cylinder is decreasing at a constant rate of 0.05 inches per second and the volume is 128pi cubic inches. At what rate is the height changing when the radius is 1.8 inches?

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.

2. Originally Posted by claybird
I have about 20 related rate problems that I just cannot get a grasp on. 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.
Recall that the volume of the sphere is defined as $\displaystyle V=\tfrac{4}{3}\pi r^3$.

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

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

Thus, we should differentiate the volume equation:

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

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

--Chris