Results 1 to 7 of 7

Math Help - volume as solid of revolution

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    19

    volume as solid of revolution

    Ok, I'm having a hard time understand this problem or what to do even.

    Two cones of height 2 and base circle of radius 4 are stuck together at their bases, and a cylindrical section of radius 2 is cut along the axis of the resulting object. Evaluate an integral to find the volume as a solid of revolution.

    Help on this would be much appreciated!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by intervade View Post
    Ok, I'm having a hard time understand this problem or what to do even.

    Two cones of height 2 and base circle of radius 4 are stuck together at their bases, and a cylindrical section of radius 2 is cut along the axis of the resulting object. Evaluate an integral to find the volume as a solid of revolution.

    Help on this would be much appreciated!
    from your description, here is a "side" view ... rotate the two red functions about the x-axis. the green line represents the side of the cylinder, whose volume will have to be subtracted.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Feb 2010
    Posts
    148
    Thanks
    2
    Quote Originally Posted by intervade View Post
    Ok, I'm having a hard time understand this problem or what to do even.

    Two cones of height 2 and base circle of radius 4 are stuck together at their bases, and a cylindrical section of radius 2 is cut along the axis of the resulting object. Evaluate an integral to find the volume as a solid of revolution.

    Help on this would be much appreciated!
    If you rotate the region bounded by the y-axis, y=2, and y=4-2x about the x-axis, you will get half of the object.

    I didn't see skeeter's post. If you turn his cone on its side you would get the one I described.

    skeeter, how did you make your drawing?
    Last edited by ione; February 21st 2010 at 12:31 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by intervade View Post
    Ok, I'm having a hard time understand this problem or what to do even.

    Two cones of height 2 and base circle of radius 4 are stuck together at their bases, and a cylindrical section of radius 2 is cut along the axis of the resulting object. Evaluate an integral to find the volume as a solid of revolution.

    Help on this would be much appreciated!
    Hi intervade,

    you could allow the y-axis to be the line passing through the vertices of both cones.
    One cone is above the x-axis, resting on it, and the other is below the x-axis,
    attached to the top cone (they are joined together).

    You can set up the situation using the following sketch
    Attached Thumbnails Attached Thumbnails volume as solid of revolution-vor6.jpg  
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jan 2010
    Posts
    19
    Ok, so just checking my work here, is this correct:


    Sorry,

    2[ Pi * integral[from 0 - 2][ (4-2x)^2 - 2^2 ]dx ] ?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Feb 2010
    Posts
    148
    Thanks
    2
    Quote Originally Posted by intervade View Post
    Ok, so just checking my work here, is this correct:


    Sorry,

    2[ Pi * integral[from 0 - 2][ (4-2x)^2 - 2^2 ]dx ] ?
    y=4-2x and y=2 intrsect at (1, 2) so your limits of integation are from 0 to 1

    As skeeter pointed out, this object would be missing the tips of the cone.
    Last edited by ione; February 21st 2010 at 06:40 PM.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by intervade View Post
    Ok, so just checking my work here, is this correct:


    Sorry,

    2[ Pi * integral[from 0 - 2][ (4-2x)^2 - 2^2 ]dx ] ?
    with limits from 0 to 1, that would be the volume of the center part rotated about the x-axis minus the cylinder's volume ...

    now the big question is, should the ends be included or not?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. volume of solid of revolution
    Posted in the Calculus Forum
    Replies: 12
    Last Post: July 3rd 2011, 05:33 AM
  2. volume of solid of the revolution
    Posted in the Calculus Forum
    Replies: 7
    Last Post: August 8th 2010, 08:01 AM
  3. volume of solid revolution around y=3
    Posted in the Calculus Forum
    Replies: 7
    Last Post: August 4th 2010, 07:02 AM
  4. volume of solid revolution
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 9th 2010, 08:54 AM
  5. volume of a solid of revolution?
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 8th 2006, 03:06 AM

Search Tags


/mathhelpforum @mathhelpforum