# Percent increase/decrease cylinder (no values)

1. Feb 6, 2010

### riskybeats

By approximately what percent would the volume of a right circular cylinder increase or decrease if the height were to increase by 2% and the radius of the base were to decrease by 1.5%?

Partial differentials makes sense in this case, I am just stuck when I have no usable values.

Volume of a cylinder = $$\pi$$r2h
dV = $$\pi$$r2dh + 2$$\pi$$r dr

dh = 1.02
dr = .985

I'm stuck in how to translate this in a comparable way to the original cylinder. Any suggestions are welcome!

2. Feb 6, 2010

### rock.freak667

When you do that divide the left side by V and the right side by πr2h and then you can find the percentage.

3. Feb 6, 2010

### Dick

No, no. dh isn't 1.02, dh/h is 0.02. And the quantity you want to find is the percentage change. That's dV/V.

4. Feb 6, 2010

### riskybeats

Okay, the only reason I did 1.02 is because I thought of doing I could express is as a negative/positive percentage. This was obviously a bad move and doesn't make any sense. But I got it now. Thanks for the help everyone!