# Homework Help: Volume of a spherical segment

1. May 14, 2009

### navybuttons

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

Use Cavalieri's Principle to find the volume of a spherical segment of one base and thinckness h if the radius of the sphere is r.

2. Relevant equations

http://img395.imageshack.us/img395/2826/sphere1.jpg [Broken]

Volume of half-sphere: 2/3$$\pi$$r2
Volume of cone inverse to half-sphere: 1/3 $$\pi$$r2

3. The attempt at a solution

I've been working this for the last three days and can't see how the answer is derived. The best I've been able to do is work out a cone with height and radius $$\alpha$$ where $$\alpha$$= r-h

But I haven't had any success this way, and question its usefulness.

If need be, I can post what the answer is supposed to be, I'm just interested in how its derived.

Last edited by a moderator: May 4, 2017
2. May 16, 2009

### larstuff

Le Cavalieris principle is about functions in the plane (2d) that are "hightened" into space (3d) by revolving them about the x-axis. A cut half circle would do here.

Last edited by a moderator: May 4, 2017