SOLUTION: THE GRAZING GOAT Zoe the goat is tied by a rope to one corner of a 15 meter by 25 meter barn in the middle of a large, grassy field. Over what area of the field can Zoe graze if

Question 40139: THE GRAZING GOAT
Zoe the goat is tied by a rope to one corner of a 15 meter by 25 meter barn in the middle of a large, grassy field. Over what area of the field can Zoe graze if the rope is:
a) 10 meters long?
b) 20 meters long?
c) 30 meters long?
d) 40 meters long?
e) Zoe is happiest when she has at least 400 m2 to graze. What possible lengths of rope could be used?

Found 3 solutions by Nate, checkley71, tomlaidlaw:
Answer by Nate(3500)   (Show Source): You can put this solution on YOUR website!
The area of the barn is: 15*25 = 375 squared meters
The area of the stretch of rope is:
because it is a fourth of the area of a circle
a) 10 meters long?

about 78.54 squared meters
I think you can do the rest with the formula presented.
e) Zoe is happiest when she has at least 400 m2 to graze. What possible lengths of rope could be used?

Answer by checkley71(8403)   (Show Source): You can put this solution on YOUR website!
A=PI*R~2 OR A=3.14*10083/4 OR A=235.5 M~2 FOR THE 10 M ROPE
A=PI*400*3/4+PI*100*1/4 OR A=1020.5 ZOE IS HAPPY WITH AT LEAST A 20 M ROPE
Answer by tomlaidlaw(14)   (Show Source): You can put this solution on YOUR website!
10m rope = 3/4*pi*10^2
20m rope = 3/4*pi*20^2 + 1/4*pi*5^2
30m rope = 3/4*pi*30^2 + 1/4*pi*15^2 + 1/4*pi*5^2
40m rope = 3/4*pi*40^2 + 1/4*pi*25^2 + 1/4*pi*15^2
next: If we have to stick with the prescribed answer choices, then 20 ft.
If not, 11.3 m does it.
A = 3/4*pi*r^2
A = 3/4*pi*11.3^2 = 401.1509
Tom Laidlaw
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