Answer to Question #178124 in Calculus for Kopano

Question #178124

A goat is tied by a rope of length r metres to the corner of a square field with sides of length 100 m,. Find r if the goat is able to reach exactly half the grass in the field.


1
Expert's answer
2021-04-15T07:40:15-0400


Find the area of the field:


"S_1=100\\cdot100=10000 m^2"

A goat is able to reach the area of a quarter of the circle:


"S_2 =\\frac{1}{4}\\pi r^2"

This area is equal to half the area of the field:


"\\frac{1}{4}\\pi r^2=5000""\\pi r^2 =4\\cdot 5000""\\pi r^2 =20000""r^2 =\\frac{20000}{\\pi}""r=\\sqrt{\\frac{20000}{\\pi}}=100\\sqrt{\\frac{2}{\\pi}}\\approx79.8 m"

Answer: The goat is able to reach exactly half the grass in the field if "r\\approx79.8 m"



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