Results 1 to 3 of 3

Math Help - Volumes of Revolution

  1. #1
    Member
    Joined
    Jul 2011
    Posts
    140

    Volumes of Revolution

    Having a bit of trouble with this one. Can anyone help me out?

    Many thanks.

    Q.
    The given diagram (see attachment) shows the line [tex]y=2x[tex]. Find the volume generated when this line is rotated about the x-axis from x=3 to x=0

    Attempt: If x=3, the height of the generated volume is also 3.
    For x=3, y=2x\rightarrow y=2(3)\rightarrow y=6. Thus, the height of the volume generated is 6.
    Volume: \pi\int^3_0y^2\,dx=\pi\int^3_0\frac{r^2(2x)^2}{h^2  }=\pi\int^3_0\frac{r^2(4x^2)}{h^2}=\pi[\frac{r^2(4x^3}{3(h^2)}]^3_0=\pi[\frac{6^2(4(3)^3)}{3(3)^2}]-\pi[\frac{6^2(4(0)^3)}{3(3)^2}]=\pi\frac{3888}{27}-0=144\pi

    Ans.: (From text book): 36\pi
    Attached Thumbnails Attached Thumbnails Volumes of Revolution-photo-2-.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Feb 2009
    From
    London
    Posts
    39
    Thanks
    1

    Re: Volumes of Revolution

    Hey,

    Have a think about the shape that is made when the line y=2x is rotated through 2\pi around the x-axis. There is a formula for calculating the volume of such a shape (hint: area=\frac{\pi r^2h}{3}, where h is height and r is radius).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jul 2011
    Posts
    140

    Re: Volumes of Revolution

    Ok, I think I see where I went wrong. Thank you.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Volumes of Revolution
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 13th 2010, 03:31 PM
  2. Replies: 6
    Last Post: February 11th 2010, 07:08 PM
  3. Volumes of Revolution
    Posted in the Calculus Forum
    Replies: 7
    Last Post: February 1st 2010, 06:23 PM
  4. Volumes of Revolution
    Posted in the Calculus Forum
    Replies: 5
    Last Post: February 26th 2009, 10:57 PM
  5. Volumes of Revolution
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 14th 2008, 02:27 PM

Search Tags


/mathhelpforum @mathhelpforum