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Math Help - The "Hungry Cow" Problem - area of circles and squares

  1. #1
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    The "Hungry Cow" Problem - area of circles and squares

    Farmer Jane tied her cow on a 15-foot tether to the corner of a shed, which measures 12 feet by 5 feet. When she returned, the cow had eaten all the grass it could reach and had become sick. Before prescribing medicine for the cow, the veterinarian wants to know how much grass the cow has eaten. How many square feet of grass has the cow eaten?


    I drew a diagram of the cow tied to the shed, but I became stuck after this. My diagram of the problem is attached. I am thinking that I may need the area of a circle, but if the cow can only reach the side of the shed because the rope will not allow the cow to go all the way around the shed, it does not make sense to have the area of a circle. Please help! Thanks!





    [IMG]file:///C:/Users/moirh/AppData/Local/Temp/msohtmlclip1/01/clip_image001.png[/IMG]




    Attached Files Attached Files
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  2. #2
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    Re: The "Hungry Cow" Problem - area of circles and squares

    Quote Originally Posted by moir View Post
    Farmer Jane tied her cow on a 15-foot tether to the corner of a shed, which measures 12 feet by 5 feet. When she returned, the cow had eaten all the grass it could reach and had become sick. Before prescribing medicine for the cow, the veterinarian wants to know how much grass the cow has eaten. How many square feet of grass has the cow eaten?


    I drew a diagram of the cow tied to the shed, but I became stuck after this. My diagram of the problem is attached. I am thinking that I may need the area of a circle, but if the cow can only reach the side of the shed because the rope will not allow the cow to go all the way around the shed, it does not make sense to have the area of a circle. Please help! Thanks!





    [IMG]file:///C:/Users/moirh/AppData/Local/Temp/msohtmlclip1/01/clip_image001.png[/IMG]




    I expect the cow is actually tied to the BOTTOM corner of the shed...
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  3. #3
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    Re: The "Hungry Cow" Problem - area of circles and squares

    I had trouble viewing your file, so I made my own diagram.



    So, the area consists of 3/4 of a circle with radius 15 and 2 quarter-circles.
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