NCSSM Distance Learning – Mathematics
The Box Problem
In the figure shown below, squares (shaded) are cut from a sheet of paper (8 ½ inches by 11
inches).
1. You and your group will be given the length of the side of each square in inches and the
materials to build the open top box. Once the squares are cut out of the paper, fold the paper into
a box that has no lid.
2. Find the dimensions and volume of the box you have built.
3. Other class members will build different boxes. Record their dimensions and volumes when
each group reports on their findings.
Size of Square
Length of Base
Width of Base
Height of Box
VOLUME
0.5 inches
1 inch
1.5 inches
2 inches
2.5 inches
3 inches
3.5 inches
4 inches
4. Plot the ordered pairs (x, y) = (Height of Box, Volume) on the graph paper on the next page.
NCSSM Distance Learning – Mathematics
The Box Problem
5. What size square should be cut out at each corner so as to produce the box with largest
volume?
6. Does this point represent the largest volume box that can be built from this paper?
7. If we want to build a box that will hold 40 cubic inches, what size should the square be that we
cut from each corner?