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Math Help - Is there enough info to do this problem?

  1. #1
    Senior Member sfspitfire23's Avatar
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    Is there enough info to do this problem?

    Given a figure of a square with a circle inscribed in it. If the area of the shaded region (the region outside of the inscribed circle) is 1, then find the area of the circle?

    A. pi/4
    B. pi
    C. pi/(pi-4)
    D.1/2(pi-4)
    E. pi/(pi-4)^2

    This is a gre quant Q
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Let's say the side of the square is x. Then, the shaded area is given by:

    x^2 - \pi (\frac{x}{2})^2 = 1

    Solve for x. Then find the area of the square
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  3. #3
    Senior Member sfspitfire23's Avatar
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    I'm trying to use (2r)^2 as the area of my square but the answer won't come out that way. Why is this?
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  4. #4
    MHF Contributor Unknown008's Avatar
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    Oops, typo from my part. You need to find the area of the circle... not the square. Sorry

    Ok,     x^2 - \pi (\frac{x}{2})^2 = 1

    So,

    x^2(1-\frac{\pi}{4}) = 1

    For ease, I'll multiply by pi and 1/4.

    \frac{x^2\pi}{4}(1-\frac{\pi}{4}) = \frac{\pi}{4}

    \frac{x^2\pi}{4} = \frac{\pi}{4(1-\frac{\pi}{4})}

    But x^2/4 * pi is the area of the circle... so;

    Area = \frac{\pi}{4-\pi}

    Simplify if need be.
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  5. #5
    MHF Contributor
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    Quote Originally Posted by sfspitfire23 View Post
    I'm trying to use (2r)^2 as the area of my square but the answer won't come out that way. Why is this?
    Should come out ok:
    4r^2 - pi r^2 = 1
    r^2(4 - pi) = 1
    Hokay?
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