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How to find the angle of a sector using the area and radius

Discussion in 'General Discussion' started by T345, Sep 30, 2013.

  1. T345

    Soldato

    Joined: Oct 14, 2011

    Posts: 5,727

    Location: Kent

    Hi guys, another maths question.
    I am having trouble finding the method to do this, online and in my head.
    The question is:
    A sector with radius 6cm has an area 70cm sq. Calculate the angle of the sector Theta.
    I am struggling, and if anyone can show me how to do it, I will be grateful.
    Thanks
    Bakht
     
  2. [FnG]magnolia

    Capodecina

    Joined: Aug 29, 2007

    Posts: 23,898

    Location: Auckland

    Go to bed homework, you're drunk.
     
  3. tomparker95

    Wise Guy

    Joined: Jan 9, 2013

    Posts: 1,447

    Location: West Sussex

     
  4. D.P.

    Caporegime

    Joined: Oct 18, 2002

    Posts: 25,135


    The answer is very easy, I will let you work it out form basic principles:
    A) What is the formula to find the area of a circle?
    b) what is the radius of the circle given in the questions?
    C) What is the fractional area of the sector given in the question?
    D) If you cut a circle n half what would the area of the 2 half be and what are the angles of the 2 sectors?
    E) Out of 360 degrees the sector must have angle with a fraction proportional to the areas.
     
  5. dowie

    Caporegime

    Joined: Jan 29, 2008

    Posts: 25,000

    42
     
  6. T345

    Soldato

    Joined: Oct 14, 2011

    Posts: 5,727

    Location: Kent

    Ok, so I got the area of the entire circle (36pi).
    The fractional area would be
    70/36pi.
    I don't know what you mean in D though :confused:
     
  7. Pom Pom

    PermaBanned

    Joined: Aug 24, 2013

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    1.21 Jiggawatts.
     
  8. fornowagain

    Sgarrista

    Joined: Nov 3, 2004

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    Location: UK

    222d
     
  9. Devrij

    Capodecina

    Joined: Jul 23, 2009

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    Location: Slaithwaite

    He's saying half a circle would be 18pi, and the angle of that sector is 180 degrees. So work out what the angle is using the fraction that 77/36pi represents.
     
  10. Elixir

    Wise Guy

    Joined: Jul 17, 2011

    Posts: 2,074

    theta/360 = 70/36pi

    The angle will be the same fraction of the entire circle as the area is.
     
  11. Hyburnate

    Capodecina

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    Location: NN4

    Yeah, dude I pity you. Maths goes straight over my head.
     
  12. JBod

    Soldato

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    Over 9000.
     
  13. DN3000

    Gangster

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    Location: UK, London

  14. SlyReaper

    Soldato

    Joined: Apr 26, 2008

    Posts: 5,908

    Location: Bristol, Old Blighty

    The area of a full circle of radius 6 is 36*pi. Yours isn't a full circle, it has area 70. So the fraction of the circle you have is 70/(36*pi). Multiply that by 360, and you have your answer in degrees. If you want to show off to your maths teacher, give the answer in radians instead.
     
  15. D.P.

    Caporegime

    Joined: Oct 18, 2002

    Posts: 25,135

    Im just trying to get you to think. If you cut a circle in half then each half would have an angle of 180 degrees which is half of 360 and the area of each half is obviously half the original entire circle.

    If you understand why that works then it is obvious how the angle of the sector and area relate to the original circle.
     
  16. Kosmiche

    Banned

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    [​IMG]
     
  17. Hodders

    Mobster

    Joined: Oct 18, 2002

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    Location: Aldbourne Wiltshire

    A circle of radius 6cm has an area of pi * 6 * 6 (pi r^2)

    The area of the cake slice is 70cm

    The proportion of the whole cake (360 degrees) is 360 * 70 / (pi * 36)

    Now please tell me that this is year 7 stuff .....
     
  18. teaboy5

    Soldato

    Joined: Jan 12, 2006

    Posts: 5,193

    Location: NI

    Year 7 really ?

    Why do people always put people down who don't understand math? Not every is great it and believe it or not, some people have little to no time for math, bar say passing it at GCSE level.
     
    Last edited: Oct 1, 2013
  19. Monkeynut

    Soldato

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    I really really had to do this. I just did.
     
  20. JBod

    Soldato

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    Gnnnnngggnnggghggggg..... MATHS.. MATHS
     


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