Question

A box without a lid will be constructed from 75 cm x 100 cm piece of cardboard, by cutting squares of the same size from each corner, and folding up the sides. What is the approximate volume of the largest possible box that can be constructed?

Answer 1

If the squares have length x, then
v = (75-2x)(100-2x)x = 4x^3 - 350x^2 + 7500x
dv/dx = 12x^2 - 700x + 7500
dv/dx = 0 at x = (175 - 25√13)/6 ≈ 14.14
So the maximum volume is about 47,380 cm^2

If you don't yet have calculus tools, then you'll need a numeric method or a graph to find the value of x needed.