Question 103797: If there is a goat tied to a rectangular barn on a 50 foot lead and the barn is 20 feet by 20 feet (floor), what is the maximum grazing area? If there are regions you can't find the area of, provide as good an estimate as you can. Assume the goat is tied to a corner outside the barn, cannot get in, and that the barn is not grazing area. (Remember, this will be based on parts of circles, no other shapes...the goat's rope will only get shorter when he tries to go around the barn...)
7. When the rope goes around the barn, what is the new radius? How much of a circle can it make without hitting the barn or overlapping area you've already found? What is that area?
8. When the rope goes around the barn the other way, what is the new radius? How much of a circle can it make without hitting the barn or overlapping area you've already found? What is that area?
9. The areas you found in 7 and 8 overlap each other. How much do they overlap? What *approximate* shape do they make? What is that area?
10. What is the total grazing area the goat can reach?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If there is a goat tied to a rectangular barn on a 50 foot lead and the barn is 20 feet by 20 feet (floor), what is the maximum grazing area? If there are regions you can't find the area of, provide as good an estimate as you can. Assume the goat is tied to a corner outside the barn, cannot get in, and that the barn is not grazing area. (Remember, this will be based on parts of circles, no other shapes...the goat's rope will only get shorter when he tries to go around the barn...)
7. When the rope goes around the barn, what is the new radius?
Ans: 30 ft at the 1st corner; 10 ft at the diagonally opposite corner.
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How much of a circle can it make without hitting the barn or overlapping area you've already found?
Ans: 1/4 of a circle
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What is that area?
Ans: (pi)30^2 = 900 pi sq. ft.
8. When the rope goes around the barn the other way, what is the new radius? How much of a circle can it make without hitting the barn or overlapping area you've already found?
Ans: 1/4 of a circle
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What is that area?
Ans: pi(30^2) = 900pi sq ft.
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9. The areas you found in 7 and 8 overlap each other. How much do they overlap?
Ans: 3/4 pi 10^2 = 75 pi sq ft.
What *approximate* shape do they make?
Ans: 3/4 of a circle of radius 10 ft.
What is that area?
10. What is the total grazing area the goat can reach?
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I'll leave that to you.
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Cheers,
Stan H.
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