SOLUTION: There's a circular field. At the edge of the field is stake. Tied to the stake is a goat What is the formula to figure how long the needs to be to allow the goat the eat exactly ha

Question 1031232: There's a circular field. At the edge of the field is stake. Tied to the stake is a goat What is the formula to figure how long the needs to be to allow the goat the eat exactly half the area of the field? Griffox24@aol.com
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The area of a semi-circle is pi * r^2 / 2
:
Suppose r is 4, then area of semicircle is 8pi
:
Let L be the length of rope tied to goat, then
:
piL^2 = 8pi
:
L^2 = 8
:
L = 2square root(2)
:
The ratio is 2square root(2) / 4 = 0.71
:
The length of rope is 0.71r, where r is the radius of the circular field

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