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.
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.
$\therefore$ Radius of the region grazed by each cow $=\frac{50}{2}=25 \mathrm{~m}$
Area that each cow grazes $=\frac{1}{4} \times \pi \times r^{2}$
$=\frac{1}{4} \times 3.14 \times 25 \times 25$
$=490.625 \mathrm{~cm}^{2}$
Total area grazed $=4 \times 490.625=1963.49 \mathrm{~m}^{2}$
Area of the square $=(\text { Side })^{2}$
$=50^{2}$
$=2500 \mathrm{~cm}^{2}$
Now,
Area left ungrazed = Area of the square $-$ Grazed area
$=2500-1963.49=536.51 \mathrm{~m}^{2}$