area of sector help

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  1. dongonaeatu's Avatar
    1 12-05-2012  23:57
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    area of sector help
    http://www.ocr.org.uk/download/pp_11...gce_475201.pdf
    question 9

    area of sector=1/2r^2 theta

    so area of sector= 1/2r^2 times pie/6 radians

    so area of sector= pie/12 times r^2

    then i dont know what to do. I need the triangle but in the marked solutions have they done the cosine rule?
  2. Intriguing Alias's Avatar
    2 13-05-2012  00:01
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    Re: area of sector help
    (Original post by dongonaeatu)
    http://www.ocr.org.uk/download/pp_11...gce_475201.pdf
    question 9

    area of sector=1/2r^2 theta

    so area of sector= 1/2r^2 times pie/6 radians

    so area of sector= pie/12 times r^2

    then i dont know what to do. I need the triangle but in the marked solutions have they done the cosine rule?
    First of all, this question is about cake not pie :ahee: (seriously though - it's pi)

    Second: You're doing right so far. That's the area of the whole slice. Now you need to work out the area of the triangle that's cut. Once you have that you know area of triangle must = 1/2 area of sector
  3. dongonaeatu's Avatar
    3 13-05-2012  00:09
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    Re: area of sector help
    (Original post by hassi94)
    First of all, this question is about cake not pie :ahee: (seriously though - it's pi)

    Second: You're doing right so far. That's the area of the whole slice. Now you need to work out the area of the triangle that's cut. Once you have that you know area of triangle must = 1/2 area of sector
    triangle=1/2r^2theta

    so i got it as 1/4r^2 but on mark scheme it says its 1/4a^2

    oh wait dw is it because the radius is a
  4. raheem94's Avatar
    4 13-05-2012  00:11
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    Re: area of sector help
    (Original post by dongonaeatu)
    http://www.ocr.org.uk/download/pp_11...gce_475201.pdf
    question 9

    area of sector=1/2r^2 theta

    so area of sector= 1/2r^2 times pie/6 radians

    so area of sector= pie/12 times r^2

    then i dont know what to do. I need the triangle but in the marked solutions have they done the cosine rule?
    The area of triangle can be found using the formula, \displaystyle \frac12 ab sinC

    So in this question it becomes, \displaystyle \frac12 \times a \times a \times sin \frac{\pi}{6} = \frac12 \times a^2 \times sin \frac{\pi}{6}


    In this question the AREA OF SECTOR = 2 X AREA OF TRIANGLE.
  5. raheem94's Avatar
    5 13-05-2012  00:12
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    Re: area of sector help
    (Original post by dongonaeatu)
    triangle=1/2r^2theta

    so i got it as 1/4r^2 but on mark scheme it says its 1/4a^2

    oh wait dw is it because the radius is a
    'a' is not the radius.

    Do a triangle has a radius?

    'a' is the length of the sides.
  6. dongonaeatu's Avatar
    6 13-05-2012  00:14
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    Re: area of sector help
    (Original post by raheem94)
    The area of triangle can be found using the formula, \displaystyle \frac12 ab sinC

    So in this question it becomes, \displaystyle \frac12 \times a \times a \times sin \frac{\pi}{6} = \frac12 \times a^2 \times sin \frac{\pi}{6}


    In this question the AREA OF SECTOR = 2 X AREA OF TRIANGLE.
    area of triangle is also = 1/2r^2sin*theta
  7. dongonaeatu's Avatar
    7 13-05-2012  00:15
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    Re: area of sector help
    (Original post by raheem94)
    'a' is not the radius.

    Do a triangle has a radius?

    'a' is the length of the sides.
    yh thats what i meant soz
  8. dongonaeatu's Avatar
    8 13-05-2012  00:21
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    Re: area of sector help
    (Original post by raheem94)
    'a' is not the radius.

    Do a triangle has a radius?

    'a' is the length of the sides.
    is the picture meant to be just the half of the cake or are we halving the picture
  9. raheem94's Avatar
    9 13-05-2012  00:23
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    Re: area of sector help
    (Original post by dongonaeatu)
    area of triangle is also = 1/2r^2sin*theta
    I think you need to watch this video to first understand the formula.
  10. Intriguing Alias's Avatar
    10 13-05-2012  00:26
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    Re: area of sector help
    (Original post by dongonaeatu)
    area of triangle is also = 1/2r^2sin*theta
    Area of sector = \dfrac{1}{2}r^2 \theta = \dfrac{1}{2}r^2(\frac{\pi}{6})

    Area of triangle = \dfrac{1}{2}ab \sin C = \dfrac{1}{2}a^2(\sin (\frac{\pi}{6})) and since sin(pi/6) = 1/2 then this = \dfrac{1}{4}a^2

    Also, the area of the triangle = 1/2 Area of sector. Solve for a.
  11. dongonaeatu's Avatar
    11 13-05-2012  00:27
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    Re: area of sector help
    (Original post by raheem94)
    I think you need to watch this video to first understand the formula.
    ok, but the area of a triangle is also 1/2r^2sintheta it says it in my book
  12. dongonaeatu's Avatar
    12 13-05-2012  00:28
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    Re: area of sector help
    (Original post by hassi94)
    Area of sector = \dfrac{1}{2}r^2 \theta = \dfrac{1}{2}r^2(\frac{\pi}{6})

    Area of triangle = \dfrac{1}{2}ab \sin C = \dfrac{1}{2}a^2(\sin (\frac{\pi}{6})) and since sin(pi/6) = 1/2 then this = \dfrac{1}{4}a^2

    Also, the area of the triangle = 1/2 Area of sector. Solve for a.
    ok, but the area of a triangle is also 1/2r^2sintheta it says it in my book

    and i got the same answer using that- 1/4a^2
  13. raheem94's Avatar
    13 13-05-2012  00:28
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    Re: area of sector help
    (Original post by dongonaeatu)
    ok, but the area of a triangle is also 1/2r^2sintheta it says it in my book
    Did you watched the video?
  14. Intriguing Alias's Avatar
    14 13-05-2012  00:29
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    Re: area of sector help
    (Original post by dongonaeatu)
    ok, but the area of a triangle is also 1/2r^2sintheta it says it in my book
    What is r? That is only true for isosceles triangles if r is the length of two equal sides of a triangle. (i.e. yes it works for this question but that isn't the general area of a triangle formula)
  15. dongonaeatu's Avatar
    15 13-05-2012  00:29
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    Re: area of sector help
    (Original post by raheem94)
    Did you watched the video?
    i am watching the video now
  16. dongonaeatu's Avatar
    16 13-05-2012  00:30
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    Re: area of sector help
    (Original post by hassi94)
    What is r? That is only true for isosceles triangles if r is the length of two equal sides of a triangle.
    i got the right answer 1/4a^2 with the formula

    area of a triangle=1/2r^2sintheta
  17. raheem94's Avatar
    17 13-05-2012  00:30
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    Re: area of sector help
    (Original post by dongonaeatu)
    ok, but the area of a triangle is also 1/2r^2sintheta it says it in my book

    and i got the same answer using that- 1/4a^2
    It should give \dfrac{a^2}4 , but i was suggesting to watch so that you understand the formula.

    The are of sector was, \dfrac{\pi r^2}{12}

    AREA OF SECTOR = 2 X AREA OF TRIANGLE.

    \displaystyle \dfrac{\pi r^2}{12} = 2 \times \dfrac{a^2}4
  18. raheem94's Avatar
    18 13-05-2012  00:32
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    Re: area of sector help
    (Original post by hassi94)
    What is r? That is only true for isosceles triangles if r is the length of two equal sides of a triangle. (i.e. yes it works for this question but that isn't the general area of a triangle formula)
    That's why i am suggesting him to watch the video and understand the formula rather than just using it without understanding.
  19. dongonaeatu's Avatar
    19 13-05-2012  00:34
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    Re: area of sector help
    (Original post by raheem94)
    It should give \dfrac{a^2}4 , but i was suggesting to watch so that you understand the formula.

    The are of sector was, \dfrac{\pi r^2}{12}

    AREA OF SECTOR = 2 X AREA OF TRIANGLE.

    \displaystyle \dfrac{\pi r^2}{12} = 2 \times \dfrac{a^2}4
    yes okay so i could use that formula

    area of triangle=1/2absinc

    but why do i times it by 2 charlie wants to give half the slice to his m8
  20. raheem94's Avatar
    20 13-05-2012  00:37
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    Re: area of sector help
    (Original post by dongonaeatu)
    yes okay so i could use that formula

    area of triangle=1/2absinc

    but why do i times it by 2 charlie wants to give half the slice to his m8
    So he wants to give half the slice, which means the complete slice(area of sector) is 2 times the triangle.

    Hope it makes sense, just think about it.
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