SOLUTION: A goat is attached to a rope 8 yards long, which is attached to the corner of a rectangular shed in a grassy field with dimensions of 5 yards by 7 yards. What is the area of the pa

Question 195972: A goat is attached to a rope 8 yards long, which is attached to the corner of a rectangular shed in a grassy field with dimensions of 5 yards by 7 yards. What is the area of the patch of grass that the goat can graze?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A goat is attached to a rope 8 yards long, which is attached to the corner of a rectangular shed in a grassy field with dimensions of 5 yards by 7 yards. What is the area of the patch of grass that the goat can graze?
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Draw a diagram of the problem. It'll help you see the problem.
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Consider a circle of radius 8 yards, 3 yards, and 1 yard.
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(3/4)(pi)(8^2) + (1/4)(pi)(3^2) + (1/4)(pi)(1^2)
(3/4)(pi)(64) + (1/4)(pi)(9) + (1/4)(pi)(1)
(192/4)(pi) + (9/4)(pi) + (1/4)(pi)
((192+9+1)/4)(pi)
(202/4)(pi)
(101/2)(pi)
(101/2)(3.14)
158.57 square yards

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