An open rectangular box with square base has a volume of 256 cubic inches. determine the equation for the volume and surface area of the box.

Let
b> the length side of the square box
h> the height of the box
SA> surface area of the box

we know that
[volume of the box]=b²*h
volume=256 in³
b²*h=256> h=256/b²> equation 1

surface area of the box=area of the base+perimeter of base*height

area of the base=b²
perimeter of the base=4*b

surface area=b²+(4*b)*h> SA=b²+4*b*h> equation 2

substitute equation 1 in equation 2
SA=b²+4*b*[256/b²]> SA=b²+1024/b> SA=(b³+1024)/b

the answer is

the formula of the volume of the box is  V=b²*h> 256=b²*h

the formula of the surface area of the box are
SA=b²+4*b*h
SA=(b³+1024)/b