Results 1 to 6 of 6

Math Help - Need help with computing the volume of a solid by revolving lines

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    5

    Need help with computing the volume of a solid by revolving lines

    How do you compute the volume of a solid formed by revolving the given region about the lines?

    the directions are:

    compute the volume of the solid formed by revolving the given region about the line

    region bounded by y=2x, y=2 and x=0 about (a) the y-axis; (b) x=1

    It has to be solved with a definite integral
    V=∫A(x)dx,a,b

    im not 100% sure how to do this, please help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member TheMasterMind's Avatar
    Joined
    Dec 2008
    Posts
    155
    Quote Originally Posted by db2dz View Post
    How do you compute the volume of a solid formed by revolving the given region about the lines?

    the directions are:

    compute the volume of the solid formed by revolving the given region about the line

    region bounded by y=2x, y=2 and x=0 about (a) the y-axis; (b) x=1

    It has to be solved with a definite integral
    V=∫A(x)dx,a,b

    im not 100% sure how to do this, please help
    A start for a)  \int \pi \frac{y}{2}^2dy=\frac{\pi}{4} \int y^2dy= \frac{\pi y^3}{12}

    A start for b) \int \pi-\pi \frac{y}{2}^2 dy=\pi \int dy - \frac{\pi}{4} \int y^2dy=\pi y-\pi \frac{y^3}{12}

    Can you finish it off?
    Last edited by TheMasterMind; February 15th 2009 at 01:36 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2009
    Posts
    5
    Thats what i needed thank you so much
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member TheMasterMind's Avatar
    Joined
    Dec 2008
    Posts
    155
    Quote Originally Posted by db2dz View Post
    Thats what i needed thank you so much
    No problem, what did you get for the final results?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Feb 2009
    Posts
    5
    (a) 2(pi)/3

    (b) 4(pi)/3
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member TheMasterMind's Avatar
    Joined
    Dec 2008
    Posts
    155
    Quote Originally Posted by db2dz View Post
    (a) 2(pi)/3

    (b) 4(pi)/3


    a)\int^2_0 \pi \frac{y}{2}^2dy=\frac{2 \pi }{3}

    <br />
b)\int^2_0 \pi-\pi \frac{y}{2}^2dy=2 \pi-\frac{2 \pi }{3}=\frac{4 \pi }{3}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: April 9th 2010, 08:26 PM
  2. volume of revolving solid
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 3rd 2009, 04:45 PM
  3. Volume - revolving solid
    Posted in the Calculus Forum
    Replies: 7
    Last Post: October 7th 2009, 03:41 PM
  4. Volume of the solid revolving about y-axis
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 4th 2009, 10:55 AM
  5. Volume of a Solid by Revolving
    Posted in the Calculus Forum
    Replies: 5
    Last Post: July 28th 2009, 10:15 AM

Search Tags


/mathhelpforum @mathhelpforum