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?

Answer 1

Each cow can graze a region that cannot be accessed by other cows.
∴ Radius of the region grazed by each cow = $\frac{50}{2}=25\mathrm{m}$

Area that each cow grazes = $\frac{1}{4}\times \mathrm{\pi }\times r^2$
$$\begin{gathered} =\frac{1}{4}\times 3.14\times 25\times 25 \\ =490.625{\mathrm{cm}}^2 \end{gathered}$$

Total area grazed = $4\times 490.625=1963.49{\mathrm{m}}^2$
$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{square}=(\mathrm{Side}{)}^2 \\ ={50}^2 \\ =2500{\mathrm{cm}}^2 \end{gathered}$$

Now,
Area left ungrazed = Area of the square $-$ Grazed area
= $2500-1963.49=536.51\mathrm{m}{}^2$