Related rates problem involving a piston (simple)

[stf]

Homework Statement

A piston is seated at the top of a cylindrical chamber with radius 5 cm when it starts moving into the chamber at a constant speed of 3 cm/s. What is the rate of change of the volume of the cylinder when the piston is 2cm from the base of the chamber?

Homework Equations

V = (pi) r^2 h

The Attempt at a Solution

So I am trying to find V'

1) V = (pi) (5)^2 h (from radius 5 cm)
2) V = 25 (pi) h
3) V' = 25 pi h' (implicit differentation)
4) V' = 25 pi (3 cm/s)(going by the chamber height, eg the top of the cylinder changes?)
5) V' = 75 pi cm^2/s

So what I am slightly unsure of, if this is correct (and I feel it probably isn't) is where exactly does the h=2 come in?

Any help is appreciated, this section is killing me :(

 

[SammyS]

It's almost right. What are units for volume? not cm².

 

[stf]

It's almost right. What are units for volume? not cm².

Yes, it should actually be cubed, thanks!

Is the actual calculus I am doing correct? Also why am I not using the base h=2? I feel I am missing something else in this problem.

 

[SammyS]

The base is uniform for a cylinder. i.e. it's a constant.

BTW: the "2 cm form bottom" is unimportant for this problem.

YES! - except for that units thing: I'm quite sure you did this correctly!

 

[stf]

The base is uniform for a cylinder. i.e. it's a constant.

BTW: the "2 cm form bottom" is unimportant for this problem.

YES! - except for that units thing: I'm quite sure you did this correctly!

Ok, thank you for the help!