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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 :(