Question 136131: The horse is tethered to a rope, at one end of a square corral(outside the corral) 10 feet on a side. The horse can graze at a distance of 18feet from the corner of the corral where the rope is tied. What is the total grazing area of the horse.
Answer by vleith(2983)   (Show Source):
You can put this solution on YOUR website! Think about the geometry of this one before you start.
Given the horse is outside a fenced in area 10 feet on a side. The horse is tethered to one corner with a rope 18 feet long. Let's use the lower right corner of the fencing.
Now imagine the horse only covers the area it can reach without kinking the rope (limit the horse to the areas it can reach below and to the right of the fencing.
If the horse walks directly left as far as the rope allows, it will be 18 feet from the corner it is tied to, and (18-10) feet from the the bottom left corner. Let's call this point A.
From point A the horse could swing up the left side of the fencing. The area he could cover would be a portion of a circle. The circle's radius would be 8 feet. And the horse could cover a quarter circle before he ran into the fence on the left hand side.
Now assume the horse is back at point A. Now have the horse walk as far out as he can the other direction (downward). His path will again be a portion of a circle. But this time the radius is 18 feet. And this time he can walk all the way around to the top right corner. At the point the rope begins to kink again. the horse is 8 feet above the top right corner post.
So the horse covered an area 3/4 of a circle 18 feet in radius.
Once the horse get to the top right corner, he swings around at another 8 foot circle above the top side of the fencing (same area as the left side).
Net the horse can cover a semicirlce of 8 feet radius plus 3/4 circle of 18 feet.
You do the math.
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