Results 1 to 2 of 2

Math Help - Need help approaching a simultaneous equation

  1. #1
    Newbie
    Joined
    Mar 2013
    From
    Maryland
    Posts
    2

    Need help approaching a quadratic, simultaneous equation

    It's been overs ten years since my last calculus course, and I think I've regressed back to a pre-algebra level. Not looking for an answer here, just help getting started.

    What I think I have here is a simultaneous equation, but I'm not sure... as I try to work it out, I keep getting stuck with what seems like a quadratic equation. I'm sure I'm wrong on one or both counts, so can someone lend some perspective?

    The problem:

    I'm trying to design a cylinder with dimensions proportional to a larger cylinder.

    The diameter of the original cylinder = 26.24 ft
    The height of the original cylinder = 12.08 ft

    This gives a diameter to height ratio of 2.172.


    I'd like to find the dimensions necessary to design a 0.668 cubic foot cylinder while maintaining the proportions of the larger cylinder, so I've come up with the following simultaneous equations:

    diameter = X (in feet)
    height = Y (in feet)

    (X/2)2 * PI * Y = 0.668 cubic feet
    X/Y = 2.172


    I've tried to solve for X in the first equation...

    X2/4 * PI * Y = 0.668
    X2 * PI * 4Y = 4 * 0.668 = 2.672
    X2 * 4Y = 2.672 / PI
    X2 = 0.2126 / 4Y
    X2
    = 0.05316 / Y
    X = SQRT (0.05316 / Y)

    ... and then insert it into the second equation...

    (SQRT (0.05316 / Y)) / Y = 2.172
    (SQRT (0.05316 / Y)) = 2.172Y
    (SQRT (0.05316 / Y))2 = 4.7176Y2
    0.05316 = 4.7176Y2 / Y
    0.05316 = 4.7176Y
    Y = 0.0113 feet

    This would make the height of the cylinder 0.135 inches, and the diameter 0.35 inches. This isn't right.

    I'm sure this is simple and that I'm making it overly complex. Still, any help would be really appreciated. Thanks!
    Last edited by Math441100; March 5th 2013 at 04:18 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    4,021
    Thanks
    741

    Re: Need help approaching a simultaneous equation

    Hey Math441100.

    One error is in this line:

    X2 = 0.2126 / 4Y

    If you try 2.672/pi you get an answer of 0.850524 and not 0.2126.

    Try using this value instead and see how you go.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Simultaneous equation help
    Posted in the Algebra Forum
    Replies: 4
    Last Post: September 27th 2012, 12:51 PM
  2. Simultaneous Equation
    Posted in the Algebra Forum
    Replies: 5
    Last Post: December 1st 2009, 03:53 AM
  3. pls help me w simultaneous equation
    Posted in the Algebra Forum
    Replies: 3
    Last Post: June 7th 2009, 09:27 PM
  4. Simultaneous equation...
    Posted in the Algebra Forum
    Replies: 7
    Last Post: December 29th 2008, 01:23 PM
  5. Simultaneous Equation
    Posted in the Algebra Forum
    Replies: 10
    Last Post: December 26th 2008, 08:11 PM

Search Tags


/mathhelpforum @mathhelpforum