Three Dimensional Box Applet: Working With Volume & Surface Area
Description
Use the applet at http://www.mste.uiuc.edu/users/carvell/3dbox/default.html to find out the size of the square corners that should be cut out to get the maximum volume for each of the paper sizes below.
This applet is great for studying the volume and surface area of a
rectangular prism and how to maximize it. The graph
simulates a piece of paper that is X units by Y units long. Drag your
cursor in the top left quadrant. Dotted lines will show how much of the
paper's corners will be cut. Click the "Cut and Fold"
button and the paper will fold into a box.
Example: Paper Size 12 by 12
Paper (X by Y)
|
Corner square
(cut out)
|
Surface
Area
|
Volume
|
Applet shot
|
| 12 by 12 |
1
|
140
|
100
|
 |
12 by 12
|
2
|
128
|
128
|
|
12 by 12
|
3
|
108
|
108
|
|
12 by 12
|
4
|
80
|
64
|
|
The maximum volume of a box has a corner square of length 2 and a volume of 128 square units.
Next try these.
Applet Source: box.java , Written by Kristen Carvell.
Last Revised: 8/3/01