Results 1 to 3 of 3

Math Help - volumes of solids by revolution

  1. #1
    Senior Member
    Joined
    Jul 2006
    From
    Shabu City
    Posts
    381

    volumes of solids by revolution

    find the volume of the solid of revolution generated by revolving about the y-axis the region bounded by the curve y = \sqrt{x}, the x-axis and the line x = 4;

    Just checking out if its:
    \pi \int_{0}^{2} (4)^2 - (4 - y^2)^2 dy ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    find the volume of the solid of revolution generated by revolving about the y-axis the region bounded by the curve y = \sqrt{x}, the x-axis and the line x = 4;

    Just checking out if its:
    \pi \int_{0}^{2} (4)^2 - (4 - y^2)^2 dy ?
    why do you have \left( 4 - y^2 \right)^2? it is the out radius, which is 4. minus the inner radius which is y^2

    your formula should be:

    \pi \int_{0}^{2} \left[4^2 - \left( y^2 \right)^2 \right]~dy


    (remember, the \pi should be applied to both radii)


    ...you know, I never noticed you were from the Philippines until now...
    Last edited by Jhevon; September 22nd 2007 at 08:25 PM. Reason: forgot to square the inner radius: thanks ticbol
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    find the volume of the solid of revolution generated by revolving about the y-axis the region bounded by the curve y = \sqrt{x}, the x-axis and the line x = 4;

    Just checking out if its:
    \pi \int_{0}^{2} (4)^2 - (4 - y^2)^2 dy ?
    outer radius = 4
    inner radius = x

    dV = pi[4^2 -x^2]dy

    y = sqrt(x)
    y^2 = x
    so,
    x^2 = y^4

    Therefore,
    dV = pi[4^2 -y^4]dy
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: February 11th 2010, 07:08 PM
  2. Volumes of Solids of Revolution - Integration
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 2nd 2009, 05:05 AM
  3. Volumes of solids of revolutions
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 27th 2009, 05:08 PM
  4. volumes of solids using integrals
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 2nd 2008, 11:07 AM
  5. Volumes of solids by slicing help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 21st 2007, 08:20 AM

Search Tags


/mathhelpforum @mathhelpforum