I don't even know where to begin...

[Jaina]

Here's the problem:

Mechanics are reboring a 6-in-deep cylinder to fit a new piston. The machine they are using increases the cylinder's radius one-thousandth of an inch every 3 minutes. How rapidly is the cylinder volume increasing when the bore (diameter) is 3.800 in?

This is as far as I've gotten (aside from drawing a picture):

.001/3= .00033 in/min

And I have no idea where to go from there. I have a feeling that there's some other formula that I need, but I have no idea what, and even if I knew it I'm not sure I'd know what to do with it.

 

[stapel]

You are given that the height h = 6, and this is fixed, so dh/dt = 0. You are also give that dr/dt = (1/3)(0.001), where "t" is measured in minutes. And you are asked for dV/dt when r = (1/2)(3.8).

What is the volume formula for a cylinder with height h and radius r?

Differentiate this formula with respect to t. Then plug in all the givens, and solve for the one remaining quantity, dV/dt.

Eliz.