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Math Help - Geometry-Circle-Cylinder help

  1. #1
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    Geometry-Circle-Cylinder help

    Hi, I'm having trouble with this problem. I've worked it, and my answer keeps getting flagged as incorrect:

    By what percent is the area of a 12.4- cm-radius circle increased if the radius is increased 1.0 cm?

    I come up with 16.8% using pi(r^2) and dividing the difference by 12.4's area. Thanks in advance!
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  2. #2
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    Hello, clockworks204!

    Looks good to me!

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  3. #3
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    Quote Originally Posted by clockworks204 View Post
    Hi, I'm having trouble with this problem. I've worked it, and my answer keeps getting flagged as incorrect:

    By what percent is the area of a 12.4- cm-radius circle increased if the radius is increased 1.0 cm?

    I come up with 16.8% using pi(r^2) and dividing the difference by 12.4's area. Thanks in advance!
    If the radius of 12.4\,\textrm{cm} is increased by 1\,\textrm{cm}, then the radius becomes 13.4\,\textrm{cm}.

    This means

    12.4k = 13.4

    k = \frac{13.4}{12.4}

    = \frac{134}{124}

     = \frac{67}{62}.

    So the magnification factor of the radius is \frac{67}{62}.


    This means the magnification factor of the area is

    k^2 = \left(\frac{67}{62}\right)^2

     = \frac{4489}{3844}

     \approx 1.16779

     = 116.779\%.


    Since you end up with 116.779\% of what you started with, the area has increased by 16.779\%.
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  4. #4
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    Thank you all for explaining. I did have the right answer rounded, but the LONCAPA program would only accept 16.779 as an answer!
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