Results 1 to 2 of 2

Math Help - volume of solid inside ellipsoid

  1. #1
    Junior Member
    Joined
    Aug 2009
    Posts
    53

    volume of solid inside ellipsoid

    hello,

    i want to find the mass of hte solid inside the ellipsoid

    [(x^2)/(a^2)]+[(y^2)/(b^2)]+[(z^2)/(c^2)]=1, if the density is |xyz|

    I make the change of variables x=ax', y=by', z=cz'
    so that (x'^2)+(y'^2)+(z'^2)=1

    so now i want

    M = abc triple integral over the volume of the sphere of |abcx'y'z'|dx'dy'dz'

    I change to cylindrical coordinates

    so now i want

    M = abc triple integral over teh volume of the sphere of |abcz'(r^2)sintcost|rdtdrdz'

    because of the aboslute value in the integral i consider the mass in one octant and then multiply by 8 the relevant limits are

    for the variable r, from 0 to 1
    for the variable t, from 0 to pi/2
    for the variable z', from 0 to 1

    i end up with [(abc)^2]/2 but book says [(abc)^2]/6

    please help i'm so v. frustrated with these cylindrical coordinates where i'm i messing things up? (i guess in the limits, but where?)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Aug 2009
    Posts
    53
    p.s.

    thank anyway but think i've got it

    the limits for r are instead: from 0 to squrt root of [1-(z'^2)]
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Volume of Solid Inside Ellipse
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 6th 2011, 09:34 PM
  2. Volume of ellipsoid
    Posted in the Calculus Forum
    Replies: 0
    Last Post: November 17th 2009, 06:26 PM
  3. Replies: 1
    Last Post: September 29th 2009, 06:09 AM
  4. Replies: 3
    Last Post: December 22nd 2008, 11:40 PM
  5. Volume of solid inside 2 spheres
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 25th 2007, 01:17 PM

Search Tags


/mathhelpforum @mathhelpforum