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Question
Four cows are tethered at the four corners of a square field of side 50 m such that each can graze the maximum unshared area. What area will be left ungrazed?
Solution
Each cow can graze a region that cannot be accessed by other cows.
∴ Radius of the region grazed by each cow `=50/2 = 25 "m"`
Area that each cow grazes`=1/4xxpixx"r"^2`
`= 1/4xx3.14xx25xx25`
= 490.625 cm2
Total area grazed = 4 × 490.625 = 1963.49 m2
Area of the square = (Side)2
= 502
= 2500 cm2
Now,
Area left ungrazed= Area of the square - Grazed area
= 2500 - 1963.49 = 536.51 m2
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