Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What's the area of this volume?

  1. Jul 24, 2004 #1
    Consider a 3d coordinate system with axis x,y and z.

    We are given a circle on the x-z plane with function [tex]z^2 + (x-a)^2 = a^2[/tex]. We rotate this circle 90 degrees around the z-axis. What's the volume of the resulting surface?
     
  2. jcsd
  3. Jul 24, 2004 #2

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Well, shouldn't that be a quarter of a torus?
    I'll opt for that and say:
    [tex]V=\pi{a}^{2}*\frac{\pi}{2}a=\frac{\pi^{2}}{2}a^{3}[/tex]

    Edit:
    The area function for a given angle measured relative to the x-axis (and with the origin as the pole) is [tex]f(\theta)=\pi{a}^{2}[/tex]

    By Cavalieri's principle, we have:
    [tex]V=\int_{0}^{\frac{\pi}{2}}\pi{a}^{2}ad\theta[/tex]
     
    Last edited: Jul 24, 2004
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: What's the area of this volume?
  1. Volumes and areas (Replies: 7)

  2. (Volume)' = Area (Replies: 16)

Loading...