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Thread: Elliptical frustum's height? Vol. is V=(1/3)*pi*{(a*b)*(bh/b-d) - (c*d)*[(bh/b-d)-h]}

  1. #1

    Elliptical frustum's height? Vol. is V=(1/3)*pi*{(a*b)*(bh/b-d) - (c*d)*[(bh/b-d)-h]}

    For
    an elliptical frustum that has the following values:
    a-base major radius
    b-base minor radius
    c-top major radius
    d-top minor radius
    h-height

    The Volume is calculated using:
    V = (1/3)*pi*{(a*b)*(bh/b-d) - (c*d)*[(bh/b-d)-h]}

    What would be the formula for finding height:
    h = ?

    Thanks in advance!


  2. #2
    Elite Member
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    Quote Originally Posted by eimimitu View Post
    For
    an elliptical frustum that has the following values:
    a-base major radius
    b-base minor radius
    c-top major radius
    d-top minor radius
    h-height

    The Volume is calculated using:
    V = (1/3)*pi*{(a*b)*(bh/b-d) - (c*d)*[(bh/b-d)-h]}

    What would be the formula for finding height:
    h = ?

    Thanks in advance!

    First thing I would do is to draw a sketch and locate those given parameters on the sketch.

    Then tell us what did you find?
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  3. #3
    Senior Member
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    Rochester, NY
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    Quote Originally Posted by eimimitu View Post
    For
    an elliptical frustum that has the following values:
    a-base major radius
    b-base minor radius
    c-top major radius
    d-top minor radius
    h-height

    The Volume is calculated using:
    V = (1/3)*pi*{(a*b)*(bh/b-d) - (c*d)*[(bh/b-d)-h]}

    What would be the formula for finding height:
    h = ?


    I don't trust the formula as given, for several reasons.

    First, it looks as if you omitted some essential parentheses, e.g. around "b-d".

    But more important, the volume should be proportional to h, and this is not apparent as I would expect in any reasonably derived formula.

    But if the formula is correct, then the answer would be found by "just" solving for h. Try factoring out h!

  4. #4

    Factoring h

    Quote Originally Posted by Dr.Peterson View Post
    [/LEFT]
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    I don't trust the formula as given, for several reasons.

    First, it looks as if you omitted some essential parentheses, e.g. around "b-d".

    But more important, the volume should be proportional to h, and this is not apparent as I would expect in any reasonably derived formula.

    But if the formula is correct, then the answer would be found by "just" solving for h. Try factoring out h!
    Thank you for pointing this out... yes the b-d should be in parenthesis on both instances...

    That's the thing I'm having trouble with is factoring out the h.. I have tried several ways but I get stuck in a loop of passing the "h" back and forth from the equal sign.

    I start with this: 3V/pi=(ab)(bh/(b-d))-(cd)(bh/(b-d))-h).. but kinda lost after that.

  5. #5
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    Quote Originally Posted by eimimitu View Post
    Thank you for pointing this out... yes the b-d should be in parenthesis on both instances...

    That's the thing I'm having trouble with is factoring out the h.. I have tried several ways but I get stuck in a loop of passing the "h" back and forth from the equal sign.

    I start with this: 3V/pi=(ab)(bh/(b-d))-(cd)(bh/(b-d))-h).. but kinda lost after that.
    3V/π=(ab)(bh/(b-d))-(cd)(bh/(b-d))-h)

    3V/π=[h * {ab2/(b-d) - (cd)(b/(b-d))-1)}]
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  6. #6

    Factoring h

    I thought I would make the proper correction to this for the next guy that needs it

    There were some errors in the formula as pointed out by Dr. Peterson(thank you).. below is the corrected one. (
    π
    represents pi... [thank you
    Subhotosh Khan]
    )
    V = (1/3)
    π
    ( (ab) (
    bh/(b-d))
    - (cd) (
    (bh/(b-d))
    -h ) )

    I solved for h like this:
    h = 3V / (cd
    π) ( ab2 / (b-d)(bd) ) - ( ( b / (b-d) ) - 1 )

    It finally clicked thanks to both of your tips so a very enthusiastic thank you!

  7. #7

    yet another correction...

    those **** parenthesis...

    h = 3V / (cdπ) [( ab2 / (b-d)(bd) ) - ( ( b / (b-d) ) - 1 )]

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