math

If the area of a circle increases by a factor of 9, by what factor does its circumference increase ?

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asked by Thomas
  1. a = pi r^2
    A = pi R^2 = 9 a = 9 pi r^2
    so
    R^2 = 9 r^2
    R = 3 r

    c = 2 pi r
    C = 2 pi R = 2 pi (3r) = 3 (2 pi r)
    so
    C = 3 c

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    posted by Damon
  2. Since A = pi*r^2
    9A = pi*(3r)^2
    That is, the radius grows by a factor of 3

    So, since C = 2pi*r, it also grows by a factor of 3.

    Just so you know, if
    the linear value grows by n,
    the area grows by n^2
    the volume grows by n^3

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    posted by Steve
  3. C= 2 pi r = 2 pi (3r) = 3 ( 2 pi r )

    so C = 3 c

    why C = 3 c I don't understand

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    posted by Thomas

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