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Math Help - Volumes

  1. #1
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    Volumes

    Ok, quite a simple Question.

    The base of a solid S is the region in the xy plane enclosed by the parabola y^2 = 4g and the line x=4, and each cross section perpendicular to the x axis is a semi-ellipse with the minor axis one-half of the major axis.

    Show that the area of the semi ellipse at x=h is pi.h
    (you may assume A = pi.ab)

    Ok, here's my question. Why is a = y and b = y/2. I dont get this
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  2. #2
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    Quote Originally Posted by noobonastick View Post
    Ok, quite a simple Question.

    The base of a solid S is the region in the xy plane enclosed by the parabola y^2 = 4g
    I presume you mean [itex]y^2= 4x[/itex]

    and the line x=4, and each cross section perpendicular to the x axis is a semi-ellipse with the minor axis one-half of the major axis.

    Show that the area of the semi ellipse at x=h is pi.h
    (you may assume A = pi.ab)

    Ok, here's my question. Why is a = y and b = y/2. I dont get this
    I assume you mean that a and b are the semi-axes of the ellipse. It would have been good to say that.

    You are told that " each cross section perpendicular to the x axis is a semi-ellipse with the minor axis one-half of the major axis". The fact that the cross section is perpendicular to the x axis tells you that the measurement is semi-axis is parallel to the y-axis so its length is just "y". The fact that the other axis is 1/2 that tells you that its length is y/2.

    I recommend you draw a picture.
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  3. #3
    Junior Member
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    Sep 2008
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    Ok, i'm really out of it today.

    In the question, they gave a picture, and i tried to work out the Volume without reading the question. Ironically, I typed up the question, but I still didnt read it.
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