Results 1 to 5 of 5
Like Tree1Thanks
  • 1 Post By Reckoner

Math Help - Find the equation for the surface of revolution by revolving

  1. #1
    Member
    Joined
    Aug 2011
    Posts
    117

    Find the equation for the surface of revolution by revolving

    Find the equation for the surface of revolution by revolving
    2z = \sqrt {4- x^2} about the x- axis

    Okay, this is far as i can get

    z = \frac {\sqrt {4- x^2}} {2}

    What should i do to solve this?
    Last edited by icelated; June 6th 2012 at 01:32 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Reckoner's Avatar
    Joined
    May 2008
    From
    Baltimore, MD (USA)
    Posts
    1,024
    Thanks
    75
    Awards
    1

    Re: Find the equation for the surface of revolution by revolving

    Quote Originally Posted by icelated View Post
    Find the equation for the surface of revolution by revolving
    2z = \sqrt {4- x^2} about the y - axis
    Are you sure that the question asks for revolution about the y-axis? Because that doesn't make a lot of sense to me. The equation 2z = \sqrt{4-x^2} defines a plane curve in the xz-plane, which would be perpendicular to the y-axis. The axis of revolution should be in the same plane as the generating curve.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Aug 2011
    Posts
    117

    Re: Find the equation for the surface of revolution by revolving

    Sorry, i meant x-axis
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Reckoner's Avatar
    Joined
    May 2008
    From
    Baltimore, MD (USA)
    Posts
    1,024
    Thanks
    75
    Awards
    1

    Re: Find the equation for the surface of revolution by revolving

    Quote Originally Posted by icelated View Post
    Sorry, i meant x-axis
    Okay, that's better.

    Let's let z = r(x) = \frac{\sqrt{4-x^2}}2. For a fixed point on this curve \left(x_0, 0, r\left(x_0\right)\right), revolving the point about the x-axis produces a circle parallel to the yz-plane whose equation is y^2+z^2=\left[r(x_0)\right]^2. Replacing x_0 with the independent variable x gives us an equation for the resulting surface of revolution:

    y^2+z^2=\left[r(x)\right]^2

    \Rightarrow y^2 + z^2 = \left(\frac{\sqrt{4-x^2}}2\right)^2

    \Rightarrow y^2 + z^2 = \frac{4-x^2}4

    \Rightarrow \frac{x^2}4 + y^2 + z^2 = 1

    As you can see from the equation, this surface is an ellipsoid.
    Thanks from icelated
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Aug 2011
    Posts
    117

    Re: Find the equation for the surface of revolution by revolving

    Thank you
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. find an equation for surface of revolution
    Posted in the Calculus Forum
    Replies: 3
    Last Post: June 6th 2012, 12:45 PM
  2. Surface of Revolution?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 26th 2010, 08:51 AM
  3. Replies: 4
    Last Post: February 17th 2010, 02:45 AM
  4. Equation of the surface of revolution?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 6th 2009, 03:46 AM
  5. Surface Area of revolving object
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 6th 2007, 03:55 PM

Search Tags


/mathhelpforum @mathhelpforum