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Math Help - Geometry - The area the goat can graze?

  1. #1
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    Geometry - The area the goat can graze?

    I need some help with this one.

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  2. #2
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    For examples (similar goat grazing) click here:

    The area the goat can graze - Google Search=
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  3. #3
    No one in Particular VonNemo19's Avatar
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    Let A_1=\pi{(15.7)}^2-\frac{\frac{\pi}{4}}{2\pi}\pi{(15.7)}^2=\pi{15.7}^  2-\frac{\pi(15.7)^2}{8}=\frac{7\pi(15.7)^2}{8} be the area the goat can graze in a circle around the pen from when the rope (fully extended) is paralel to BC until it is parallel to AB.

    Let A_2=\frac{1}{4}\pi{(15.7-\sqrt{162})^2} be the remaining quarter circile the goat can graze after its tether makes contact with point A.

    Then the area the goat can graze is given by:

    A_1+A_2=...
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  4. #4
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    Quote Originally Posted by VonNemo19 View Post
    Let A_1=\pi{(15.7)}^2-\frac{\frac{\pi}{4}}{2\pi}\pi{(15.7)}^2=\pi{15.7}^  2-\frac{\pi(15.7)^2}{8}=\frac{7\pi(15.7)^2}{8} be the area the goat can graze in a circle around the pen from when the rope (fully extended) is paralel to BC until it is parallel to AB.

    Let A_2=\frac{1}{4}\pi{(15.7-\sqrt{162})^2} be the remaining quarter circile <<< (?) the goat can graze after its tether makes contact with point A.

    Then the area the goat can graze is given by:

    A_1+A_2=...
    I don't want to pick at you but I've got a slightly different result:

    The remaining sector with radius r \approx 3 has the area:

    A_2=\dfrac{\bold{\color{red}3}}{\bold{\color{red}8  }}\pi{(15.7-\sqrt{162})^2}

    But probably I have misunderstood the question - as usual ...
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  5. #5
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    Agree with Earboth (maybe we both misunderstood!).

    p = pi ; r = 15.7 ; h = sqrt(162)

    A = (p/8)(10r^2 - 6hr + 3h^2) = ~687.9812
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  6. #6
    No one in Particular VonNemo19's Avatar
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    Yeah, earboth is right. I gave it the old college try though.
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