1. Not finding help here? Sign up for a free 30min 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!

Derive the volume of a sphere.

  1. Oct 19, 2005 #1
    The forumula for 2¶r can intergrated to make ¶r^2 (at least I think). So can anyone derive the volume of a sphere
    4/3¶r^3?
     
  2. jcsd
  3. Oct 19, 2005 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    First thing: the volume of a sphere is...0.

    Second: to find the volume of a ball seen as a domain in [itex] \mathbb{R}^{3} [/itex], one could antidifferentiate the expression giving the surface of the ball as a function of its radius.

    Daniel.
     
  4. Oct 19, 2005 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

     
  5. Oct 19, 2005 #4
    to derive the volume of a sphere I think you want to start with the unit ball in 3 space. Then convert to spherical coordinates and integrate the triple intergral. I think im close, I remember doing this a while back so take it FWIW.
     
  6. Oct 20, 2005 #5
    Why not try a surface of revolution? For example, take a semi-circle and rotate it around the x-axis to find the volume.

    [tex]\text{V}=\pi\int_{a}^{b}f(x)^2\,dx[/tex]
     
  7. Oct 21, 2005 #6
    I solved this out for practice on my own. I found the volume of a revolved surface. I said [tex]\text{V}=\pi\int_{r}^{-r} (\sqrt{r^2 - x^2})^2dx[/tex].
    I'm pretty sure that should work thus giving you a simple to evaluate integral of
    [tex]\pi\int_{r}^{-r} \(r^2 -x^2)dx[/tex].
    Should be easy enough. If you have trouble with understanding whereabout the integral came from, realize that it is simply the sum of the volume's of cylinders.
    (Note: I hope I typed that latex code right...I've never used it before. Sorry if it comes out wrong.)
     
    Last edited: Oct 21, 2005
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Derive the volume of a sphere.
  1. Volume of Sphere (Replies: 3)

  2. Volume of a sphere (Replies: 2)

  3. Volume of sphere (Replies: 8)

  4. Volume of sphere (Replies: 13)

Loading...