Consider x cm as the length cut off from each corner

So the length of box is (12 – 2x) cm and x cm as its breadth and height

Here volume can be written as

V = (12 – 2x)^{2} × x

On further simplification

V = 4x^{3} – 48x^{2} + 144x

By differentiating w.r.t. x

We know that V is maximum when x = 2

Here V = {(12 – 4)^{2} × 2} = {64 × 2} = 128 cm^{3}