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Proving area with radians

  1. Feb 17, 2008 #1
    in a circle with perimeter of 20cm a sector has radius r, angle θ radians and area Acm^2
    prove that A= 25-(r-5)^2

    A=1/2 r^2 θ
    c=2Πr

    the only thing that I can think to do is c=2Πr therefore 20=2Πr
    10=Πr r=10/Π
    so then A=1/2 r^2 θ
    =1/2 (10/Π)^2 θ
    = θ (100/2Π^2)
     
    Last edited: Feb 17, 2008
  2. jcsd
  3. Feb 17, 2008 #2
    Why don't you post the entire question again, and in a neat way, it will make life easier for everybody here, and surely you will get more responses!

    EDIT: you can just edit the first post, and delete the others, or ask a PF to delete the others.
     
    Last edited: Feb 17, 2008
  4. Feb 17, 2008 #3
    i can't seem to get the 2s to show up superscript...is there a particular way?
     
  5. Feb 17, 2008 #4
    you might want to use LATEX if you are familiar with that at all? or you can just do it
    r^2, and we will know that r is raised to the power of 2.
     
  6. Feb 17, 2008 #5
    thanks, i hope this is better
     
  7. Feb 17, 2008 #6

    HallsofIvy

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    Honestly, it looks to me like that statement is not true and so cannot be proved. For one thing, it does not involve "[itex]\theta[/itex]" and that can't be right.
     
  8. Feb 18, 2008 #7
    I believe that the statement should have been like this:

    A sector of a circle has a perimeter of 20cm and a area of "A" and the circle has a radius of "r". Prove that "A = 25-(r-5)(r-5)"

    Now with simple methods, show that the arc of sector is (20-2r). Find the angle of sector in terms of "r". Then substitute the angle to the area of sector and it is proved easily.
     
  9. Feb 18, 2008 #8

    HallsofIvy

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    If you are not given the angle, how could you possibly prove that the length of the arc of the sector is 20- 2r? The length obviously depends on [itex]\theta[/itex].
     
  10. Feb 18, 2008 #9
    Indeed it does, but the perimeter also allows to find the Arc length, since the perimeter is the addition of the three sides (Arc length and two radii):

    (Length of Arc) + (2 * radius) = Perimeter of Sector

    or, Length of Arc = Perimeter of Sector - (2 * radius)

    or, Length of Arc = 20 - 2r
     
  11. Feb 18, 2008 #10

    HallsofIvy

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    OH! The original post read "a circle with perimeter of 20cm" and when you changed it to "A sector of a circle has a perimeter of 20cm " I was still thinking about the circled and just thought about the length of the arc.
     
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