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Volume of a spherical segment

  • #1

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 [Broken]

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

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 [tex]\alpha[/tex] where [tex]\alpha[/tex]= 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:

Answers and Replies

  • #2
16
0

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 [Broken]

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

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 [tex]\alpha[/tex] where [tex]\alpha[/tex]= 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.
 
Last edited by a moderator:

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