Related Rates

[winterrose]

So I am stuck on this related rate problem. I also think I am over thinking it. But this is the question: A piston is compressing a gas contained in a cylinder. Given that the pisotn is moving into the cylinder at 10cm/sec, and the diameter of the cylinder is 6cm, at what rate is the volume of the gas changing?

There is a picture of a cylider with V=V(t) and below that x=x(t)

So I am looking for V(t). And I know that V(cylinder)=pi*r^2*h, than I take the derivative except I dont knkow what the qty for h is? I am only given: dia=6cm, and dr/dt=(10cm/sec). Would I treat h as a constant? Thanks for any advice.

 

[stapel]

When the piston moves (up and down) in the cylindrical cylinder, the height changes. The height of the "chamber" (the open area inside the cylinder) can not be "constant"!

We can't see the picture you're looking at. How is "x(t)" defined?

 

[winterrose]

So I am stuck on this related rate problem. I also think I am over thinking it. But this is the question: A piston is compressing a gas contained in a cylinder. Given that the pisotn is moving into the cylinder at 10cm/sec, and the diameter of the cylinder is 6cm, at what rate is the volume of the gas changing?

There is a picture of a cylider with V=V(t) and below that x=x(t)

So I am looking for V(t). And I know that V(cylinder)=pi*r^2*h, than I take the derivative except I dont knkow what the qty for h is? I am only given: dia=6cm, and dr/dt=(10cm/sec). Would I treat h as a constant? Thanks for any advice.

Ended up figuring this out. Thanks for the response.

But r^2 was the constant and dh/dt=(-10cm/sec)

dv=(pi)(r^2)(dh/dt)
dv=(pi)(3^2)(-10)

and solve for dv