Box Folding: Questions

Main Page | Folding Boxes | Gathering Data | Organizing Data | Using the Applet | Questions | Formulas and Graphs

Here are some questions for students in different classes.

General questions

- How can you be convinced that you have found the biggest possible volume?

- If you're convinced that you've found it for a 22 x 19 piece of grid paper, how would you find it for an 8.5" x 11" piece of letter paper? Put the data in a spreadsheet and check the answer using the box folding applet for 8.5 x 11.

- Think of the height as a variable "x", and express the volume of the box made from 22x18 grid paper in terms of x.

- What does the graph of equation look like? Graph it using a
graphing
calculator. For help, there is a page
with the output.

- Explain what is happening with the boxes when the graph dips
below the x-axis.

- Take the equation y = 4x
^{3}- 80x^{2}+ 396x and find the local maxima betwen 0 and 9.

- How does this relate to the volume of the boxes?

- Come up with a general formula for the volume of a box created in this way, given L (the length of the original rectangle) and W (the width of the original rectangle).

- Examine the spreadsheet of data from the different sized papers that were used in the applet and come up with some questions of your own.