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Math Help - Circular Plot

  1. #1
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    Circular Plot

    The circumference of a circular plot of land is increased by 10%. What is the best estimate of the total percentage that the area of the plot increased?
    (1) 10% (3) 25%
    (2) 21% (4) 31%


    The answer is 21%. I have no idea how to even start this question.

    I know that A = pi(r^2) and C = pi(d)

    This question makes no sense to me.

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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by magentarita View Post
    The circumference of a circular plot of land is increased by 10%. What is the best estimate of the total percentage that the area of the plot increased?
    (1) 10% (3) 25%
    (2) 21% (4) 31%


    The answer is 21%. I have no idea how to even start this question.

    I know that A = pi(r^2) and C = pi(d)

    This question makes no sense to me.

    well, if the circumference increases by 10% it means the radius increases by that amount, right? so r \to 1.1r

    now A = \pi r^2

    let r \to 1.1r

    then A \to \pi (1.1r)^2 = 1.21 \pi r^2

    so A \to 1.21 A. in other words, it increases by 21%
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  3. #3
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    great

    Quote Originally Posted by Jhevon View Post
    well, if the circumference increases by 10% it means the radius increases by that amount, right? so r \to 1.1r

    now A = \pi r^2

    let r \to 1.1r

    then A \to \pi (1.1r)^2 = 1.21 \pi r^2

    so A \to 1.21 A. in other words, it increases by 21%
    A great reply.
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