Answer:
4 inches deep by 16 inches square (the cut square is 4 inches)
Step-by-step explanation:
If x is the side of the square cut from each corner, the folded depth of the box is x, and the dimensions of the square base are 24-2x on each side. Then the volume is ...
V = x(24-2x)^2
The derivative of volume with respect to x is ...
dV/dx = (24-2x)^2 +x(2)(24-2x)(-2) = (24-2x)(24 -6x)
Values of x that make this zero are 24/2 = 12 and 24/6 = 4. The latter value is the one of interest.
The box is 4 inches deep and 16 inches square.
