SOLUTION: A pony is tethered to one corner of a 20 -foot by 40- foot barn in the middle of a large grassy field. The rope is 50 feet long. Over what area can the pony graze.(he can't go in t

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: A pony is tethered to one corner of a 20 -foot by 40- foot barn in the middle of a large grassy field. The rope is 50 feet long. Over what area can the pony graze.(he can't go in t      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1034618: A pony is tethered to one corner of a 20 -foot by 40- foot barn in the middle of a large grassy field. The rope is 50 feet long. Over what area can the pony graze.(he can't go in the barn, and there isn't any grass in there..)
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Not too tough to draw a reasonable diagram on paper.

The pony can go into three regions:

A sector of 270 degrees of radius 50 which gives %28270%2F360%29%2Api%2A50%5E2 square feet; this is %283%2F4%29pi%2A2500;

Smaller sector of a circle of 90 degrees and radius 10 feet giving %281%2F4%29pi%2A10%5E2 square feet;

Medium sector of a circle of 90 degree, radius 30 feet to give %281%2F4%29pi%2A30%5E2;

The SUM of these area regions.


----
The pony can stretch the tether line 50 feet along one wall of 40 feet, leaving 10 feet more to stretch along the next wall.
The ponly can stretch the tether line 50 feet along the other wall of 20 feet leaving 30 more feet to stretch along the next wall.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the barn is 20 by 40.
the pony is tethered to one corner of the barn.
the length of the rope is 50.
the area of a circle is equal to pi * r^2.
the length of the rope is equal to r, which is the radius of the circle.
for 3/4 of the circle, he has the full radius of the rope at his disposal.
the area covered is 3/4 * pi * 50^2 = 3/4 * pi * 2500 = 7500/4 * pi = 1875 * pi square feet.
he has 30 foot radius of a circle left that was formed from the opposite corner on the 20 foot side.
the area he can cover, that has not already been covered, is 1/4 * pi * 30^2 = 1/4 * pi * 900 = 225 * pi square feet.
he has 10 foot radius of a circle left that was form from the opposite corner on the 40 foot side.
the area he can cover, that has not already been covered, is 1/4 * pi * 10^2 = 1/4 * pi * 100 = 25 * pi square feet.
the total area he can cover is:
1875 * pi square feet plus ...
225 * pi square feet plus ...
25 * pi square feet plus ...
equals 2125 * pi square feet.
that's equal to approximately 6675.884388878square feet.
the diagram of the area he can cover is shown below:
$$$