# Volume of a cap of a sphere

1. Oct 24, 2007

### samee

1. The problem statement, all variables and given/known data
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

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

3. 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?

2. Oct 24, 2007

### 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?