Billy the goat is tied to the corner of Patty�s barn. The barn is 20 x 40 feet, and the rope is 50 feet long. No trees or other obstructions are in the way. What is the available area of grass that Billy can eat? (Draw a good picture of this area first.)
Billy’s (unchewable) rope is anchored at B.
He can range through
¾ of a circle, radius 50,
¼ of a circle, radius 30, and
¼ of a circle, radius 10.
¾
(50)2 + ¼(302) + ¼(102)
=(1875 + 225 + 25)
= 2125 ≈ 6676 ft2.
He can range through
¾ of a circle, radius 50,
¼ of a circle, radius 30, and
¼ of a circle, radius 10.
¾
(50)2 + ¼(302) + ¼(102)=
(1875 + 225 + 25)= 2125
≈ 6676 ft2.
This is about the same as a square 82 feet on a side or a bit more than 8 times the area of the barn.
Can you do it but 25 X 40
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