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.
- How can you be convinced that you have found the biggest
- 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
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 = 4x3 - 80x2 +
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).