Rectangular sheet of metal 750mm by 300mm - find length of the sides of the squares to give max volume to the box, and find maximum volume of the box?

with height x mm,

v = (750-2x)(300-2x)x
= 4(x^3-525x^2+56250x)

dv/dx = 12(x^2-350x+18750)
dv/dx = 0 at x=175±25√19

now pick the one which provides a max, not a min.