Question

Four cows are tethered with ropes of equal lengths at 4 corners of a square field of side 35 metres so that
they just can reach one another. Find the area left ungrazed by the cows.


please solve this question pleasr fast

Answer 1

Given:

Four cows are tethered at four corners of a 35m long square field and each cow can reach upto another cow to graze.

To find:

We need to find the area ungrazed by the cows.

Solution:

We need to observe a field and four cows tied at four corners of field such that each cow can only touch each other.

We know, length of the field is 35 metres, so we can conclude that the length of the rope of each cow is $17.5$ metres from above statement.

Now,

To find the area ungrazed = Area of the square - Area grazed by cows.

Let us move step by step and first the find area of square.

Area of square =  $a^2$

                          =  $35^{2}$

                          =  1225  $m^{2}$

Now to find area grazed by cows,

Here we need to visualize that one cow can graze the area upto $\frac{1}{4}th$ of the area of circle with radius 17.5m.

1 cow graze the area = $\frac{1\\}{4}$ × $\pi r^{2}$

∴ 4 cows graze the area = 4 × $\frac{1\\}{4}$  × $\pi r^{2}$

                                          = $\pi r^{2}$

                                          = $3.14 \times 17.5 \times 17.5$

                                          = $961.625$ $m^{2}$

Area ungrazed =  Area of the square - Area grazed by cows.

                          = $1225 - 961.625$ $m^{2}$

                          = $263.375$ metres

So, the area ungrazed by the cows is $263.375$ m.