How Is the Volume of a Spherical Segment Calculated Using Cavalieri's Principle?

[navybuttons]

Homework Statement

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.

Homework Equations

http://img395.imageshack.us/img395/2826/sphere1.jpg

Volume of half-sphere: 2/3\pir²
Volume of cone inverse to half-sphere: 1/3 \pir²

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.

 

[larstuff]

Homework Statement

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.

Homework Equations

http://img395.imageshack.us/img395/2826/sphere1.jpg

Volume of half-sphere: 2/3\pir²
Volume of cone inverse to half-sphere: 1/3 \pir²

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.

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.