Please write your answer along with a few lines of reasoning as a comment below, within the next 1 hour.

There are two different cloth cutting methods. In the first method, n circular pieces are cut from a square cloth piece of side a in the following steps: the square of side a is divided into n smaller squares, not necessarily of the same size, then a circle of the maximum possible area is cut from those smaller squares. In the second method, only one circle of maximum possible area is cut from the square of side a and the process ends. The cloth pieces remaining after cutting the circles are scrapped in both methods. The ratio of the total area of cloth scrapped in the former to that in the latter is...

##### Nancy verma - Apr 18, 2023

first we consider the square of side x , then its area will be x^2

now, we will cut the largest circle possible from the square of side x. So, radius of the circle is x/2

Area of circle = π(x/2)^2 = (πx^2)/4

area scrapped = x^2 - (πx^2)/4 = x^2 (1-π/4)

Hence, The area scrapped/area of square = x^2 (1-π/4)/x^2

= 1-π/4 = constant

As the ratio is constant, whether we cut a circle from smaller square or larger square, scrapped area will be a fixed percentage of square. Therefore, in this case where two squares are of the same size, the ratio will be 1:1.

##### Sumanth paul - Apr 18, 2023

The area of the portions scrapped in both the methods is same and equal to a^2*(1-pi/4).