Thread: 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.

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 .

We are given

We want to find when .

Thus, we should differentiate the volume equation:



We know and . Now it should be easy to find

--Chris