a goat needs to eat 1/2 of the grass in a circular field but must be pinned outside what diameter rope is used

Question

a goat needs to eat 1/2 of the grass in a circular field but must be pinned on the outside what diameter rope do u need? exactly 1/2 of the grass

Answer 1

Since area of a circle is: A= pi x r2 and the original area is irrelevant, and pi is a constant, you need to calculate the square root of r square over 2 to get the half.
In other words, take r (which is 1/2 of d) and divide it by the square root of 2. Take that result and multiply it by 2 to get back to the resulting diameter of the circle that must be controlled by the length of the rope.
The rope length will be the same as the radius.
(NOT the rope diameter. The diameter of the rope must be irrelevant to this question. The rope diameter would be the thickness of the rope. It needs to be thick enough to keep the goat from chewing through the rope. )

Answer 2

tie the goat exactly at the centre keeping the length of rope exactly r/sqrt 2.............r is the radius of larger circle ( the circular field)