Four cows are tethered to the four corners of a square field of length 28 m so that each cow can just touch the two cows in the adjacent corners. If the grass in the area inside the square field that was accessible to the cows was enough to feed them for 22 days, for how many days would the grass that is beyond the reach of these cows to be able to feed them if someone cuts its and leaves it inside the grazable parts? [Use $$\pi$$ = 22/7]​

Correct option is A

Given:

Length of square field= 28 cm

Each cow can just touch the two cows in the adjacent corners

The grass in the area inside the square field that was accessible to the cows was enough to fee them for 22 days

Formula used:

Area of square = $$a^2$$​​

Area of sector of circle = $$\pi r^2 \left(\frac{\theta}{360}\right)$$​​

Solution:  

​

Area of remaining part = Area of square field - Area of 4 sectors of circle

​$$\begin{aligned}&\Rightarrow (28)^2 - 4 \times \pi \times (14)^2 \times \left(\frac{90^\circ}{360^\circ}\right) \\&\Rightarrow 784 - 4 \times \pi \times 196 \times \left(\frac{1}{4}\right) \\&\Rightarrow 784 - \left(\frac{22}{7}\right) \times 196 \\&\Rightarrow 784 - 22 \times 28 \\&\Rightarrow 784 - 616 = 168 \, \text{m}^2\end{aligned}$$​​

Now we have,

Area inside the square field that was accessible to the cows (i.e. area of 4 sectors) was enough to fee them for 22 days

​$$616 \longrightarrow 22\\1\longrightarrow \frac{22}{616}\\128 \longrightarrow \frac{22}{616}\times 128= 6$$​​

Hence,  the remaining area is enough to feed the cows for 6 days.