There are 4 horses grazing at each corner at each corner of a square field of side 63m. They are roped in such a way that they can touch the middle of each side. Find the remaining area of the ground where they do not graze.( Use $$\pi = \frac{22}{7}$$​)

Correct option is C

Given:

Length of side of square field = 63m

4 horses grazing at four corners

Formula Used:

Area of square = $$a^2$$​​

Area of sector = $$\frac{\theta}{360} \times \pi \times r^2$$​​

Where a is side of square and r is radius of circle

Solution:

Here horses grazing such that they touch the middle point of the side hence forming four equal quadrant

Area of square field = $$63^2 = 3969 \ m^2$$​​

Radius of one quadrant = $$\frac{63}{2}\ m$$​​

Area of field grazen by horses = $$4 \times$$​ Area of one quadrant

$$= 4 \times \frac{90}{360}\times \frac{22}{7} \times \left(\frac{63}{2}\right)^2$$​​

​$$= 3118.5m^2$$​​

Remaining area = $$3969 - 3118.5 = 850.5m^2$$​​