G R A Z I N G A R E A
Farmer Jones had a goat on a tether. He tied the end of the tether not
attached to the goat to a stake in the field. In the field, there are a shed that is 20 feet long and 20
feet wide, which is a square, and a silo that is 20 feet in diameter. The center of the shed and the center
of the silo are on a line and the distance apart is 92 feet.
When the goat moves to M, which is on the center of one of the sides of shed, the figure shows the shape of the grazing area. The shape of the grazing area is a semicircle with a little area out of it.
The diameter of the silo is 20 feet, so the radius of silo is 10 feet. The length of tether is 76.7 ft.
d = 20 ft r = 10 ft L = 76.7 ft
When the goat is at the end of his tether on the silo side of the tangent point N, the tether runs along the silo until some point O. Then, the going goes off in a straight line, and the remainder of the tether lies on the tangent to the circle at O.
Consider the central angle between N and O, and let’s call this angle θ radian.
Hence, the area that the goat can graze is approximately 7520.29 ft.
The total area that the goat can graze as follows:
Therefore, the total area that the goat can graze is approximately 29548.53 ft2.