The side of a square is 25 cm. It is divided into n squares identical small squares. In each small square a circle is drawn touching all the four sides of it. Find the portion of the large square which is not covered by these circles.

Answer:
Side of square = 25 cm

So,
Every small square have side = $\frac{25}{n}$    cm
So,
Diameter of encircle of the small square = $\frac{25}{n}$  cm
Then,
Radius of each circle = $\frac{25}{2n}$    cm

So, Area of one circle =  $\pi {\left(\frac{25}{2n}\right)}^2$   
total number of circle  = n $\times$ n   = n​²
So area covered by all circle =  ​$\pi {\left(\frac{25}{2n}\right)}^2$   ​$\times$ n​²

= $\pi$ ( ​156.25 )
= ​491.0714  cm²
And
Area of big square = 25 ​  ​$\times$   25  = 625    cm²
So,
The portion of the large square which is not covered by these circles = 625  - 491.0714  

=  ​133.9286     cm²                              ( Ans )