Calculating the Area of a sector to mm^2

Discussion in 'Math' started by Biggsy100, Jul 22, 2014.

  1. Biggsy100

    Thread Starter Member

    Apr 7, 2014
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    I need to calculate a sector of an area. As understand it, it can be calculated as Area x 2 Pi (- Sector).

    In the case of the PDF file I have attached would read; 45mm X 2*Pi (-15mm). If I a correct, it just seem to straight forward?
     
  2. djsfantasi

    AAC Fanatic!

    Apr 11, 2010
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    Where did you get that formula from? I would approach it as follows.

    First calculate the area of the ring (as if it was an entire circle, not the segment shown).

    Area = 2*Pi*45mm - 2*Pi*30mm
    Edit: This is not the equation for area. To see the correct equation, look at studiot's post following.

    Then, since the sector only takes up Pi/2, the final area is 1/4 of the ring { (Pi/2)/(2*Pi) or (0.5*Pi)/(2*Pi) = 0.5/2 = 1/4.}

    You may be able to combine the two steps, but I think in steps. First, I k now how to do that, then I need to do the other thing... (old mathematicians joke).
     
    Last edited: Jul 22, 2014
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  3. studiot

    AAC Fanatic!

    Nov 9, 2007
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    Not sure what is going on here.

    Area is not measured in mm but in millimetres squared.

    So any formula based on the length of the circumference of a circle will fail.

    If you want the shaded area between the two part circles then yes


    calculate the area of the large circle,
    subtract the area of the smaller circle
    divided the result by four since you only want a quarter of it.



    Area = \frac{{\pi r_1^2 - \pi r_2^2}}{4} = \frac{\pi }{4}\left( {r_1^2 - 1*r_2^2} \right)

     = \frac{\pi }{4}\left( {{{45}^2} - {{30}^2}} \right) = \frac{\pi }{4}\left( {2025 - 900} \right) = 883.1m{m^2}
     
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  4. djsfantasi

    AAC Fanatic!

    Apr 11, 2010
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    D'oh... I knew the point I was trying to make, but was suckered in by the OP's original equation without thinking...

    Thanks for the clarification!
     
  5. Biggsy100

    Thread Starter Member

    Apr 7, 2014
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    1
    Ok great, however I am a little confused with the area so I put in pi/4 (2/1*-1*x2/2) = 0.7853 ?
     
  6. djsfantasi

    AAC Fanatic!

    Apr 11, 2010
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    I don't understand your equation!? Let's start with do you know the equation for the area of a circle?

    Area_{circle} = \pi * radius^{2}

    In your problem, we have the following.

    Area_{bigcircle} = \pi * 45^{2}
    Area_{smallcircle} = \pi * 30^{2}

    The difference between the two gives you the area of the ring.

    Area_{ring} = \pi * 45^{2} -  \pi * 30^{2}

    But you only want a segment of the ring, equal to \pi/2 radians

    Ratio_{segment} = (\pi / 2) / 2\pi = 0.5\pi/\2pi = 0.5/2 = 1/4

    So applying this ratio to the ring area, we get (what studiot posted):

    Area_{segment} = \frac{\pi * 45^{2} -  \pi * 30^{2}}{4}
     
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