Cut out four congruent squares from a cardboard, so that the remaining part can be folded to create the box (with no top) having max volume. (applet in Italian)
This problem can be seen from two points of view:
- the first is mainly analytic: using a suitable variable (the square side length), students calculate and investigate the function expressing the box volume (high school level - precalculus)
- the second is mainly experimental: using a suitable variable (the square side length) students can calculate the box volumes corresponding to different values of the variable. The collection of these data pairs (variable, volume) in the Spreadsheet, allows an easy creation of a bar chart. By exploring the bar chart, students can guess the variable value that yields the maximum volume of the box (middle school and over).
