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Math Help - Ratio of Circles

  1. #1
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    Ratio of Circles

    I thought the ratio would be 5:2 since both circles had the same radius, but my textbook says it is 7:2. ???
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    Re: Ratio of Circles

    Quote Originally Posted by castle View Post
    I thought the ratio would be 5:2 since both circles had the same radius, but my textbook says it is 7:2. ???
    In the graph on the left the major sector is \frac{7}{12} of the total area.

    In the graph on the right the minor sector is \frac{1}{6} of the total area.
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    Re: Ratio of Circles

    The area of the major sector in A is \displaystyle \frac{210}{360}\cdot \pi r^2 while the area of the minor sector in B is \displaystyle \frac{60}{360} \cdot \pi r^2.

    Clearly the sector in A is 2.5 times that of the area in B, so the ratio is 2.5 : 1, or 5 : 2. I agree with your answer.
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    Re: Ratio of Circles

    Quote Originally Posted by Plato View Post
    In the graph on the left the major sector is \frac{7}{12} of the total area.

    In the graph on the right the minor sector is \frac{1}{6} of the total area.
    While I agree with what you have written, one must ask whether the question was asking you to compare the area of the sectors to the total area of the circle, or whether to compare the areas of the sectors to each other. If it is the former, I would say the ratio is 7 : 2. If it is the latter I would say the ratio is 5 : 2.
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    Re: Ratio of Circles

    The question says: “What is the ratio of the areas of the major sector in diagram A to the area of the minor sector in diagram B?”

    Quote Originally Posted by Prove It View Post
    Clearly the sector in A is 2.5 times that of the area in B, so the ratio is 2.5 : 1, or 5 : 2. I agree with your answer.
    The area of major sector in A is 3.5 times the area of minor sector in B.
    Last edited by Plato; June 26th 2011 at 09:25 AM.
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    Re: Ratio of Circles

    Crap, so it is. Then the ratio is 7 : 2. Thanks
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    Re: Ratio of Circles

    for equal radii ratio of area of sectors = ratio of central angles

    = 210 : 60 ( note that central angle of major sector of circle A is 210

    = 7 : 2
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    Re: Ratio of Circles

    Quote Originally Posted by castle View Post
    I thought the ratio would be 5:2 since both circles had the same radius, but my textbook says it is 7:2. ???
    You are not given the angle of the major sector for circle A.
    You are given the angle of the minor sector of circle A.
    The ratio of the minor sectors is 5:2 since you can fit 2 and a half minor sectors from B
    into the minor sector of A.

    First find the angle of the major sector of circle A.
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  9. #9
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    Re: Ratio of Circles

    Oh my, I misinterpreted the question. Yes, 7:2 it is.
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