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?

Answer 1

Step 1: Solve the area grazed by the cows

• Given: side of square$\left(s\right)=50m$
• Radius of quadrants$\left(r\right)=$half of side of the square$=\frac{50}{2}$

Area grazed by a cow $=$ area of a quadrant

$$\begin{gathered} =\frac{1}{4}\mathrm{\pi }{\left(\mathrm{r}\right)}^2 \\ =\frac{1}{4}\mathrm{\pi }\times {\left(25\right)}^2 \end{gathered}$$

Area grazed by $4$ cows$=4\times$area grazed by $1$ cow

$$\begin{gathered} =4\times \frac{1}{4}\mathrm{\pi }\times {\left(25\right)}^2 \\ =\frac{22}{7}\times 625 \\ =1964.29m \end{gathered}$$

Step 2: Solve for the area left un-grazed

Area of square plot $={\left(side\right)}^2$

$={\left(50\right)}^2$

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

$$\begin{gathered} =\left({50}^2\right)-1964.29 \\ =2500-1964.29 \\ =535.71m^2 \end{gathered}$$

Hence, the area was left un-grazed$=535.71m^2$.