Let 'x' and 'y' represent the dimensions of the rectangle.

2x + 2y = 36

x + y = 18

y = 18 - x

The volume of the box is:

V = x*y*4

V = x*(18 - x)*4

V = -4x^2 + 72x

We need to find the value of x for which the parabolic function V = -4x^2 + 72x has maximum.

Since the quotient in front of x^2 is -4 < 0 the function has maximum for

x max = -b/(2a), where a a = -4, and b = 72

x max = -72/(2*(-4))

x max = 9 cm

y = 18 - 9 = 9 cm

The dimensions that give the maximum volume are: the rectangle is square with side length of 9 cm.