Results 1 to 4 of 4

Thread: Rotation aorund x-axis (volume)

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    51

    Rotation aorund x-axis (volume)

    Ok, this one is stumping me, I keep getting negative volume.

    find the volume of the solid generated by revolving the region enclosed by the triangle with verticies (2,2) (2,4) (8,4) about the x-axis.

    So I made a picture, found r(y)=2 and R(y)=y/3 (I did rise over run for the line, and solved in terms of y)
    so i know its the integral $\displaystyle (pi) (R(y)^2)-(r(y)^2)$

    found my bounds, 2 to 4, did the algebra, found anti deriv. and evaluated on the bounds, but I got $\displaystyle -160pi/27$ $\displaystyle units^3$
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,854
    Thanks
    138
    Quote Originally Posted by BCHurricane89 View Post
    Ok, this one is stumping me, I keep getting negative volume.

    find the volume of the solid generated by revolving the region enclosed by the triangle with verticies (2,2) (2,4) (8,4) about the x-axis.

    So I made a picture, found r(y)=2 and R(y)=y/3 (I did rise over run for the line, and solved in terms of y)
    so i know its the integral $\displaystyle (pi) (R(y)^2)-(r(y)^2)$

    found my bounds, 2 to 4, did the algebra, found anti deriv. and evaluated on the bounds, but I got $\displaystyle -160pi/27$ $\displaystyle units^3$
    1. The line y = 4 (from x = 2 to x = 8) rotating around the x-axis generates a cylinder.

    2. The line $\displaystyle y = \dfrac13x + \dfrac43$ (from x = 2 to x = 8) generates a frustrum which is taken off from the cylinder.

    3. Therefore the volume is:

    $\displaystyle V_{rot}=\int_2^8\left(\pi (4)^2 - \pi\left(\dfrac13x + \dfrac43 \right)^2 \right)dx$

    I've got $\displaystyle V=40\pi$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2008
    Posts
    51
    Thanks, I see where you got that, but I just made a huge mistake, it should be around the y-axis...dooH!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,854
    Thanks
    138
    Quote Originally Posted by BCHurricane89 View Post
    Thanks, I see where you got that, but I just made a huge mistake, it should be around the y-axis...dooH!
    Then the volume is:

    $\displaystyle V-{rot}=\int_2^4\left(\pi\left(3y-4\right)^2-\pi(2)^2 \right)dy$

    I've got $\displaystyle V=48\pi$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solid Volume rotation around y-axis
    Posted in the Calculus Forum
    Replies: 7
    Last Post: Oct 12th 2011, 09:09 AM
  2. Replies: 2
    Last Post: May 11th 2011, 01:25 PM
  3. Volume of rotation (y-axis)
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Feb 1st 2010, 05:51 PM
  4. Replies: 3
    Last Post: Sep 11th 2009, 07:53 PM
  5. volume by rotation about x axis
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Nov 26th 2008, 05:12 AM

Search Tags


/mathhelpforum @mathhelpforum