Results 1 to 2 of 2

Math Help - volume of a solid

  1. #1
    Member
    Joined
    Nov 2009
    Posts
    94

    volume of a solid

    hi
    i cant seem to make head or tail of this question. here it goes;
    find the volume of the solid generated by rotating the area enclosed by the curve y= 2-x^2 and the line y = 1, about y=1.
    i am not sure how to start. can someone please explain?
    thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,553
    Thanks
    1423
    Start by drawing the region. You should find that your area of integration is the "top" of the parabola, from \displaystyle y = 1 upwards and between \displaystyle x = -1 and \displaystyle x = 1.

    Now, if you were going to rotate this region about the line \displaystyle y = 1, you would have circular cross sections that have the same radius as the height of that region, so \displaystyle r = 2 - x^2 - 1 = 1 - x^2.

    The area of each circular cross section is \displaystyle \pi r^2 = \pi(1 - x^2)^2 = \pi(1 - 2x^2 + x^4).

    The volume will be the sum of all these cross sections over the region \displaystyle x = -1 and \displaystyle x = 1. This sum converges on an integral.

    So the integral you are evaluating is

    \displaystyle V = \int_{-1}^1{\pi(1 - 2x^2 + x^4)\,dx}.
    Last edited by mr fantastic; December 27th 2010 at 06:10 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Volume of a solid
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 26th 2010, 04:51 PM
  2. Volume of a solid
    Posted in the Calculus Forum
    Replies: 5
    Last Post: September 26th 2008, 05:03 PM
  3. volume of solid without f(x)
    Posted in the Calculus Forum
    Replies: 6
    Last Post: February 29th 2008, 05:03 PM
  4. volume of a solid
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 24th 2007, 06:31 PM
  5. Volume of Solid
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 29th 2006, 06:49 PM

Search Tags


/mathhelpforum @mathhelpforum