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    How would I go about doing this question?

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    I obviously can't use the answer to work it out and I thought that I would have to find the area of the smaller sector and minusing it from the bigger sector but I don't have theta... arghh, help please?
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    (Original post by RoseBrilliante)
    I obviously can't use the answer to work it out
    Can't you?
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    The area of a segment is equal to theta/2pi * area of the whole circle.
    Knowing that, you can work out the areas of the shaded segments in terms of theta, set them equal, and solve.
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    (Original post by Mr M)
    Can't you?
    My teacher said that I can't and that I have to work it out as if they didn't give me that bit of information :/
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    (Original post by RoseBrilliante)
    My teacher said that I can't and that I have to work it out as if they didn't give me that bit of information :/
    You don't need to substitute the value but, if this were a real examination question, you could.
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    (Original post by RoseBrilliante)
    I thought that I would have to find the area of the smaller sector and minusing it from the bigger sector but I don't have theta..
    Well, of course you don't have theta, you want to find theta to be equal to the value given ^^
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    (Original post by aznkid66)
    Well, of course you don't have theta, you want to find theta to be equal to the value given ^^
    What I'm saying is that I have no idea how to go about showing that theta equals that value :/
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    (Original post by RoseBrilliante)
    What I'm saying is that I have no idea how to go about showing that theta equals that value :/
    Follow the hint in post 3

    Remember that algebra is all about using unknown variables (like theta) as if you knew their value to make equations that may seem meaningless. ^^
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    (Original post by aznkid66)
    Follow the hint in post 3

    Remember that algebra is all about using unknown variables (like theta) as if you knew their value to make equations that may seem meaningless. ^^
    Ahh, I didn't see that post: I will try now
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    (Original post by RoseBrilliante)
    What I'm saying is that I have no idea how to go about showing that theta equals that value :/
    You need to write down all the facts you have at your disposal. So:

    LeftShadedArea = RightShadedArea
    LeftShadedArea + RightNonshadedArea = Area of small circle
    RightNonshadedArea + RightShadedArea = Area of large sector

    Can you convert these into equations using the radii that you are given and the unknown angle theta?
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    (Original post by Mr M)
    You don't need to substitute the value but, if this were a real examination question, you could.
    For A-level, you cannot assume the answer in 'show that' questions, however, you can in 'verify' questions.
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    (Original post by YThursday)
    For A-level, you cannot assume the answer in 'show that' questions, however, you can in 'verify' questions.
    I'm an A Level examiner. You can.
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    (Original post by Mr M)
    I'm an A Level examiner. You can.
    Ooh, wow. My maths teacher always insists that you cannot. Maybe it depends on the exam board? We do OCR MEI, who do you mark for?
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    (Original post by YThursday)
    Ooh, wow. My maths teacher always insists that you cannot. Maybe it depends on the exam board? We do OCR MEI, who do you mark for?
    OCR. Your maths teacher is teaching you proper mathematics - it is bad form to work backwards but we try to award marks where we can so starting with the angle and finishing with equal areas would receive full credit.
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    (Original post by Mr M)
    OCR. Your maths teacher is teaching you proper mathematics - it is bad form to work backwards but we try to award marks where we can so starting with the angle and finishing with equal areas would receive full credit.
    I can sort of see your reasoning, but I would not tend to publicize this. Although the angle-to-area argument is reversible in this case, I can see all sorts of dangers for people who don't understand how if-and-only-if conditions should be tested in general.
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    (Original post by davros)
    I can sort of see your reasoning, but I would not tend to publicize this. Although the angle-to-area argument is reversible in this case, I can see all sorts of dangers for people who don't understand how if-and-only-if conditions should be tested in general.
    Don't worry, I have no plans for a major newspaper ad campaign.
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    (Original post by Mr M)
    Don't worry, I have no plans for a major newspaper ad campaign.
    Haha - I think there's a good case for a major newspaper campaign: "Students taught wrong way to do things. Civilization on point of collapse."
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    (Original post by Slumpy)
    The area of a segment is equal to theta/2pi * area of the whole circle.
    Knowing that, you can work out the areas of the shaded segments in terms of theta, set them equal, and solve.
    (Original post by davros)
    You need to write down all the facts you have at your disposal. So:

    LeftShadedArea = RightShadedArea
    LeftShadedArea + RightNonshadedArea = Area of small circle
    RightNonshadedArea + RightShadedArea = Area of large sector

    Can you convert these into equations using the radii that you are given and the unknown angle theta?
    (Original post by Mr M)
    You don't need to substitute the value but, if this were a real examination question, you could.
    This is what I ended up doing (on the left-hand side):

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    (Original post by RoseBrilliante)
    This is what I ended up doing (on the left-hand side):

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    that's fine.

    In terms of the language I used in my earlier post, this is what I did:
    LeftShaded + RightNonShaded = area of small circle = pi(r^2) = 16pi (using r=4) (i)
    RightNonShaded + RightShaded = sector area = (1/2)R^2(theta) = 18theta (using R = 6) (ii)
    But RightShaded = LeftShaded so we also have:
    RightNonShaded + LeftShaded = 18theta (iii)

    Comparing (i) and (iii) tells us that 16pi = 18theta, or theta = (16pi/18) = 8pi/9.
 
 
 
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