V = πr2h
But she didn't stop there. She asked herself and the class:
Why is that the formula?
She went on to describe how it's like taking a bunch of CDs and stacking them. We know we can find the area of a CD.
That's when things got interesting. I heard comments like these:
- We use the height to determine how many circles it takes to make up the cylinder.
- But it's just like a line [it has no height]. How do you get volume with that?
- If you have a thing of CDs and stack them...you're going from 2D to 3D.
- But area has no height. We're stacking things that have no height.
So we talked a little about finding the volume of a rectangular prism is just counting the number of cubic units it takes to fill the prism and how doing that with a cylinder is tough because its round. I liked the direction they were going with this by trying to talk about something larger by defining it by its smaller parts. So small, in fact, that the height is practically 0.
I ask, So how can you find the volume of a sheet of paper?
A student takes a sheet of paper puts a ruler up to it as if he's going to measure the height of one sheet of paper and one of his group members says:
Dude, why don't we just make a stack that's 1" tall and divide by the number of sheets it took to make it?
They all agreed that would work and I thought we were ready to move on when a boy asks, "So what's the volume for a sphere?"
They wrestle with this for a minute or two when one of them turns to me and says, "Mr. Cox, you know, huh?"
But you're not going to tell us are you?
A student opens his planner to the Math Formulas page and starts to tell us what the formula is when one says,
I don't care what the formula is. I want to know why that's the formula.
Next semester's gonna be fun.