A rectangular piece of cardboard 18 cm \times 24 cm is made into an open box by cutting a square of 5 cm side from each corner and building up the side. What is the volume of the box? (in cm$^3$)

Original cardboard: 18 x 24 cm. After cutting 5 cm squares from each corner, the new dimensions of the box base are: length = 24 - 5 - 5 = 14 cm, width = 18 - 5 - 5 = 8 cm, height = 5 cm (the folded-up sides). Volume = length x width x height = 14 x 8 x 5 = 560 cm³. The key insight is that cutting squares from corners reduces both dimensions by twice the square's side length.