What is the Largest –
Volume, Open –Top,
Rectangular Box You can
make from….
a sheet of paper,
a piece of poster board
a sheet of cardboard….
Making the box
• You can get many sheets of paper and try
many different x’s. You can cut and fold
repeatedly and find the x by trial and error.
For your first x – let’s say x = 0.5 inch, then try
1.0 inch, and repeat as necessary to find the
largest volume.
11 inches
8.5 inches
x
Try it on the internet
Try it: http://mste.illinois.edu/users/carvell/3dbox/
Each time you click the “cut and fold” button,
the applet folds up the box and tells you its
volume and surface area.
By trial and error, find the x that produces the
largest volume.
Let’s
make a
chart:
(Use your
Graphing
Calculator)
X-value
Length
Width
Volume of
Box
(in inches)
(in inches)
(in inches)
L1
L2
L3
L4
0.0
0.5
1.0
1.5
11.0
8.5
0.0
10.0
9.0
8.0
7.5
6.5
5.5
37.5 in 3
58.5 in 3
66.0in 3
2.0
2.5
3.0
7.0
6.0
5.0
4.5
3.5
2.5
63.0in 3
52.5in 3
37.5in 3
3.5
4.0
4.0
3.0
1.5
0.5
21.0in 3
6.0in 3
What is the maximum volume of
the box according to this chart?
What happens if our increment gets
smaller?
What do we need to change?
Is there a faster way to accomplish this?
Write the function and
determine its domain.
The function is .........
V  x   x  8.5  2 x 11  2 x 
Domain is...................  0, 4 