Four horses are tethered at four corners of a square plot of side 42 meters so that they just cannot reach one another. The area left ungrazed is
Solution
Correct Answer: Option D
The length of the rope tied to the horses should each be equal to half of the side of the square plot so that they just cannot reach one another.
∵ side of the square = 42 m,
Length of the rope = 42/2 = 21 m
The area grazed by each horse should be equal to the area of sector with radius 21 m (length of the rope)
Total area covered by the four horses = 4 × (area of sector of radius 21 m and central angle 90°)
Total area left ungrazed = (Area of square field) – (Total area covered by four horses)
∴Total area left ungrazed \(= \;{42^2}\;-\;4\; \times \left( {\frac{{90}}{{360}} \times \;\frac{{22}}{7}\; \times \;21\; \times \;21} \right)\)
⇒ Total area left ungrazed = 1764 – 1386 = 378 m2
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