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Question

Four cows are tethered at four corners of a square plot of side 50m, so that they just cannot reach one another. What area will be left un-grazed?


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Solution

Step 1: Solve the area grazed by the cows

  • Given: side of square(s)=50m
  • Radius of quadrants(r)=half of side of the square=502

Area grazed by a cow = area of a quadrant

=14πr2=14π×252

Area grazed by 4 cows=4×area grazed by 1 cow

=4×14π×252=227×625=1964.29m

Step 2: Solve for the area left un-grazed

Area of square plot =(side)2

=(50)2

Area left un-grazed =area of square plot-area grazed by the cows

=502-1964.29=2500-1964.29=535.71m2

Hence, the area was left un-grazed=535.71m2.


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