Given as the side length of big square is 18 cm
Suppose the side length of each small square be a.
By cutting a square from each corner and folding up the flaps we will get a cuboidal box with
Length, L = 18 – 2a
Breadth, B = 18 – 2a and
Height, H = a
Assuming, the volume of box, V = LBH = a (18 – 2a)2
Condition for the maxima and minima is
Thus, a = 3 will give maximum volume.
And the maximum volume, V = a(18 - 2a)2 = 432 cm3