The Grass Is Greener On the Other Side
A goat is tethered with a rope of length 10 ft to the middle of a side of a fenced field whose dimensions are 5 ft x 10 ft. The entire field is covered with grass. The goat grazes on the entire area within its reach within the fenced area. There is an infinite amount of grass beyond the fence which the goat cannot reach.
What is the ratio of the area that the goat can graze to the extra area it could graze if the fence wouldn't have been there, to three decimal places?