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!

Find The Volume of A Solid

  1. Dec 1, 2011 #1
    1. The problem statement, all variables and given/known data

    find the volume of the solid bounded by the graphs of the given equations:

    r=1+cos∅
    z=y
    z=0
    (the first octant)

    2. Relevant equations

    V=[itex]\int[/itex][itex]\int[/itex] rdrd∅


    3. The attempt at a solution

    So, I've been having trouble deciding what to integrate from and to. I converted the z equations into polar coordinates, so, z=rsin and z=0

    [itex]\int[/itex][itex]^{2\pi}_{0}[/itex][itex]\int[/itex][itex]^{1+cos∅}_{0}[/itex] (rsin)rdrd∅

    Mod note: revised LaTeX
    [tex]\int_0^{2\pi} \int_0^{1 + cos(\theta)} rsin(\theta) r~dr~d\theta[/tex]

    I found, from the first integration, [2∏]\int[/0][itex] r^(3)sin∅/3 d∅ and I need to plug in (1+cos∅) and 0 for r....but, this seems WAY too complicated having a trig function to the 3rd power.

    I'm not even sure if I have the beginning correct. Can anyone help me out?
     
    Last edited by a moderator: Dec 1, 2011
  2. jcsd
  3. Dec 1, 2011 #2

    Astronuc

    User Avatar

    Staff: Mentor

    In three dimensions, the first quadrant has x ≥ 0, y ≥ 0, z ≥ 0, and think about the limits of ∅ for x ≥ 0, y ≥ 0.

    Think about this - http://www.wolframalpha.com/input/?i=polar+plot+r=1+cos+theta (don't worry about the angle being theta)

    And do you want to use cylindrical or spherical coordinates?
     
    Last edited: Dec 1, 2011
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Find The Volume of A Solid
Loading...