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Math Help - circumfrence and area

  1. #1
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    Question circumfrence and area

    In figure below, R is the midpoint of NP. If the circumference of circle N is 75.36, what is the area of circle P?
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  2. #2
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    Quote Originally Posted by sanee66 View Post
    In figure below, R is the midpoint of NP. If the circumference of circle N is 75.36, what is the area of circle P?
    Hello,

    the circumference of circle N is calculated by

    c_N = 2 \pi R


    Now the radius of circle P is: r = \frac{1}{2} R

    Now plug in this term into the formula to calculate the circumference:

    c_P = 2 \pi r = 2 \pi \left( \frac{1}{2} R \right) = \pi R

    That means the circumference of circle P is half as long as the circumference of circle N.

    EDIT:
    Thus r = 75.36 / 2 = 37.68.

    The area of a circle is calculated by: a = \pi ~r^2

    Plug in the value for r into this formula and you'll get:

    a_P = \pi \cdot 37.68^2 \approx 4460.3779...
    Last edited by earboth; July 19th 2007 at 09:13 PM. Reason: forgotten to calculate the area
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