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Question
Four cows are tethered at the four corners of a square field of side 50 m such that the each can graze the maximum unshared area. What area will be left ungrazed?
Solution
Let r be the radius of the circle.
Thus, we have ;
`r = 50/2 "m"`
= 25 m
Area left ungrazed = (Area of the square) - 4(Area of the sector where r = 25 m and θ = 90°)
`=|(50xx50)-4(3.14xx25xx25xx90/360)|"m"^2`
`=|2500-(4xx(19625)/4)|"m"^2`
`=(2500 - 1962.5) "m"^2`
= 537.5 m2
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