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Math Help - Circle Geometry - area of segment.

  1. #1
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    Circle Geometry - area of segment.

    Iam having trouble getting the correct ans of 7.16m
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    Here is a picture of the way I would try this problem. I would evaluate the area of the segment, and subtract the area of the triangle. Of course, to do this, you need to know the size of the angle.
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    Super Member Quacky's Avatar
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    With your shorthand notation, I can't even comprehend the question, but why did you use A=\pi~r^2 to find the area of A1? A1 isn't a circle!
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    basically the area i have shaded is 7.87m^2.
    the vertical height of the shaded area has to be half the height of the radius to the circle.
    I need to find the radius of the circle hence then the diameter.
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  5. #5
    Super Member Quacky's Avatar
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    Quote Originally Posted by heatly View Post
    basically the area i have shaded is 7.87m^2.
    the vertical height of the shaded area has to be half the height of the radius to the circle.
    I need to find the radius of the circle hence then the diameter.
    I understand your method, but the quoted A=\pi~r^2 formula only applies to full circles. It cannot be used to find an area of a segment, sector, etc. Or am I misinterpreting your logic? It seems to me that you are assuming that you can use the '0.5R' as a radius and the given area of the segment of 7.87 to find the radius of the whole circle.
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    ok ,yes i was assuming that-oops.
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    Quote Originally Posted by heatly View Post
    basically the area i have shaded is 7.87m^2.
    the vertical height of the shaded area has to be half the height of the radius to the circle.
    I need to find the radius of the circle hence then the diameter.
    1. You probably found the correct solution already. If not, here are the steps:

    a) Calculate the value of the central angle of the sector:

    \cos\left(\frac12 \alpha\right=\dfrac{\frac12 R}{R}=\frac12~\implies~\frac12 \alpha = 60^\circ. So the complete central angle is 120.

    b) The shaded area is a segment.

    area_{segment}=area_{sector} - area_{triangle}

    7.87 = \frac13 \cdot \pi R^2 - \frac12 \cdot R \cdot \underbrace{R \cdot \sin(120^\circ)}_{\text{height of triangle}}

    7.87 = \left(\frac13 \pi - \frac14 \sqrt{3} \right)R^2

    Solve for R.

    c) the diameter is 2R.
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    Thanks for that
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  9. #9
    Grand Panjandrum
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    If you want anymore help with this create a new thread and this time if you must post a PDF with a scan of the question MAKE SURE IT IS THE RIGHT WAY UP

    CB
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