What is the error in finding the volume of a cap of a sphere using integration?

[samee]

Homework Statement

Find the volume of a cap of a sphere with radius r and height h.
A picture of it is given here;
http://sjc.ilrn.com/ilrn/bca/user/appletImage?dbid=1276286560

Homework Equations

The area of a circle is $$\pi\$$r^2

The Attempt at a Solution

So I flattened the sphere into a circle and solved me equation for x;
x=sqrt(r^2-y^2)
Then I rotated it around the y-axis and integrated to find;
$$\pi$$$$\int$$$$\stackrel{h}{r}$$(r²-y²)dy= $$\pi$$((1/3)h³+(2/3)r³-hr²)

But the computer program I do my homework on tells me that it wrong. Now I'm confused. What did I do wrong?

 

[Dick]

As h->0 the volume should go to zero, right? Does yours? That's a clue something is wrong. Look at your limits of integration again. Are they right?