Question 1191127: a fence encloses a square field whose sides measure 10m a horse is tethered to a rope that is attached to a corner post of the field so that the horse is outside the fence. If the rope holding the horse is 18m long (the radius), find the total grazing area for the horse in square metres.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Draw this out. The horse has 3/4 of the area of a circle with radius of 18 m. That part is relatively straightforward. The area is π*18^2*(3/4)=243 pi m^2.
But if the horse stays along the fence and goes down the next side, it is like being on an 8 m tether for 1/4 of a circle. There are 2 ways this can happen. The area of a circle with an 8 meter radius is 64π m^2, and there are 2 (1/4) circles, so that is like a 1/2 circle, or 32π m^2
The total area is 275 π m^2.
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