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 (in inches)

Length(in inches)

Width(in inches)

Volume of Box

L1 L2 L3 L4

0.0 11.0 8.5 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

6.5

7.5 37.5 in 3

9.0

10.0

58.5 in 3

66.0in 3

63.0in 3

52.5in 3

37.5in 3

21.0in 3

6.0in 3

8.0

7.0

3.0

4.0

5.0

6.0

2.5

1.5

0.5

3.5

4.5

5.5

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 .........

8.5 2 11 2V x x x x

Domain is................... 0, 4