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Math Help - area of an "oval"

  1. #1
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    area of an "oval"

    Hello

    I want to calculate the area under the length "L" of this shape.
    W, h and b are known.

    I am using the formula for a ellipse, pi*h*L/4 but it is not so good when h gets bigger for instance or when b gets smaller.
    When h is small, the calculated area with the elipse equation gets to big, and when h gets larger the calculated area get smaller than it really is..


    Any ideas or tips ?
    Attached Thumbnails Attached Thumbnails area of an "oval"-oval.gif  
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  2. #2
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    Quote Originally Posted by danielel View Post
    Hello

    I want to calculate the area under the length "L" of this shape.
    W, h and b are known.

    I am using the formula for a ellipse, pi*h*L/4 but it is not so good when h gets bigger for instance or when b gets smaller.
    When h is small, the calculated area with the elipse equation gets to big, and when h gets larger the calculated area get smaller than it really is..


    Any ideas or tips ?
    "Under the length L"? Do you mean that the overall length of the figure is L and the height is h?
    That figure can best be approximated by a rectangle with a half circle on
    each end. In order that the half circle fit on the end of the rectangle its radius must be h/2. (In your picture there appears to be a small oddly region
    between the rectangle and half circle that I am ignoring. That's why this is an approximation.) The area of the two half-circles together is [itex]\pi r^2= \pi h^2/4[/itex] and the area of the rectangle is hL. The area of the entire figure is approximately [itex]hL+ \pi h^2/4[/itex].
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  3. #3
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    Sorry, the length L is just w-2b.
    h is the height in the middle of the "oval".
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  4. #4
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    Then replace my L by w- 2b. Again, since I have assumed a rectangular middle, that is only an approximation, how good the approximation is depends on there being very little change in the height for that part.
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  5. #5
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    Yes, of course.

    But what if the height does change and gets noticable smaller? is there any way to calculate the area under L then?
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