Rotations of Functions

So I am in BC Calc in my high school and we started rotations of functions. Now, the way i see it, a cylinder should be able to be evaluated to a rectangular prism, with r=l, and h=h, and then seeing as a full rotation is 2PI w=2PI. But it doesn't work for the rectangle. Can Anyone tell me where I've gone wrong?

Ummm... wot?

Let's see:
calculus and rotations of functions
cylinder and rectangular prism
r = 1
h = h
2πw = 2π

???

Don't know what your saying but I'll go ahead and show you how to find the volume of a cylinder with:
calculus and rotations of functions
a rectangle
radius = 1
height = h

Firstly, the volume of integration of function f(x) between a and b rotated around the x-axis: V = π∫(y)²dx,a,b

OK now then. To find your volume i'm going to rotate f(x)=h around the y-axis between 0 and 1.

Here's a crappy diagram (WARNING CRAPPY DIAGRAM IS CRAPPY):
,,,,,,,___,,,,,,..
,,,,,--,[b]|[/b],--,,,,..
,,,,/,,,[b]|___[/b]\,,,<h
,,,,\,,,[b]|[/b],,,[b]|[/b],,,..
,,,,|--_[b]|[/b]_--[b]|[/b],,,..
,,,,|,,,[b]|[/b],,,[b]|[/b],,,..
,,,,|,,,[b]|[/b],,,[b]|[/b],,,..
,[b]--------------[/b],<0
,,,,\,,,|,,,/,,,..
,,,,,--___--,,,,..
,,,,,,,,,,,,,,,,..
........^...^...
........0...1...
The axis and rectangle we will rotate are bold.

Now the volume we want to find is (since this is around the y-axis we swap the y to x, dx to dy and the a and b values to 0 and h):
V = π∫(x)²dy,0,h

Since the x value is 1 throughout, x=1
V = π∫(1)²dy,0,h
V = π∫1dy,0,h
V = π[y],0,h
V = π(h - 0)
V = πh

Working out the volume of a cylinder with radius = 1 and height = h normally to make sure it's correct:
V = πr²h
V = π×1²h
V = π×1×h
V = πh

Have fun!