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Math Help - Is this a simultaneous, quadratic equation? What am I doing wrong?

  1. #1
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    Is this a simultaneous, quadratic equation? What am I doing wrong?

    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
    Multiply LHS and RHS by 4 to clear demoninator
    X2 * 4PI * 4Y = 2.672
    Divide both sides by 4PI
    X2 * 4Y = 2.672 / 4PI
    X2 * 4Y = 0.2126
    Divide both sides by 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
    Multiply RHS by Y to clear denominator
    (SQRT (0.05316 / Y)) = 2.172Y
    Square both sides
    (SQRT (0.05316 / Y))2 = 4.7176Y2
    0.05316 / Y = 4.7176Y2
    Multiply both sides by Y
    0.05316 = 4.7176Y3
    Y3 = 0.0113 feet
    Y = 0.224 feet

    This would make the height of the cylinder 2.69 inches, and the diameter 5.84 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 04:06 PM.
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    Re: Is this a simultaneous, quadratic equation? What am I doing wrong?

    Quote Originally Posted by Math441100 View Post
    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!
    The second equation for X: You have an extra 4 on the RHS.

    The fourth equation for Y: You need to multiply both sides of the equation to clear out the denominator on the RHS. It looks like you divided.

    -Dan
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