1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Volume of a spherical segment

  1. May 14, 2009 #1
    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[tex]\pi[/tex]r2
    Volume of cone inverse to half-sphere: 1/3 [tex]\pi[/tex]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 [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: May 4, 2017
  2. jcsd
  3. May 16, 2009 #2
    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook