An open box with a volume of 1500 cm cube is to be constructed by taking a piece of cardboard 20 cm by 40 cm, cutting squares of side length x cm from each corner, and folding up the sides. Find the exact dimensions of the box.

The dimensions of the box formed will be:

width: 20 - 2x

length: 40 - 2x

height: x

Volume = width x length x height

1500 = x (20 - 2x) (40 - 2x)

1500 = x (800 + 4x² - 120x)

1500 = 4x³ - 120x² + 800x

0 = 4x³ - 120x² + 800x - 1500

0 = x³ - 30x² + 200x - 375

Solving the cubic equation:

x = 5 (only integer root)

Length = 30 cm

Width = 10 cm

Height = 5 cm