# Thread: function/ rate of change problem

1. ## function/ rate of change problem

The height of an (axially symmetric) pipe z as a function of the distance from the
axis of symmetry is $\displaystyle z = 2 - 2x^{2}$ , where both z and x are measured in metres, and where $\displaystyle 0 \leq z \leq 2$ and $\displaystyle 0 \leq  x  \leq 1$ . What is the total volume of hay in cubic metres
in the haystack?

This question makes no sense to me,How does 'haystack' come into this, surely it talking about a pipe?

Any help appreciated.

2. Is there more to the problem? A proceeding paragraph if it's from a textbook? It does seem out of place to suddenly go from talking about a pipe to mentioning a haystack. Unless it is referring to to x and z as dimensions for hay stacked into the pipe.

3. Originally Posted by moderata
Is there more to the problem? A proceeding paragraph if it's from a textbook? It does seem out of place to suddenly go from talking about a pipe to mentioning a haystack. Unless it is referring to to x and z as dimensions for hay stacked into the pipe.

That is the whole question, I will ask my teacher tomorrow, maybe there is a typo?

Thank you

4. I asked my teacher and he said it should say 'cylinder', instead of 'pipe' and the correct answer is $\displaystyle \pi$

I think I am meant to use Volumes of Revolution ? Any idea's as to how to start this off?