What is the Largest –Volume, Open –Top, Rectangular Box You can make from….

1. 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….

2. 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

3. 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.

4. Let’s make a chart: (Use your Graphing Calculator) 10.0 7.5 37.5 in 3 9.0 6.5 58.5 in 3 66.0in 3 8.0 5.5 7.0 4.5 63.0in 3 6.0 3.5 52.5in 3 5.0 2.5 37.5in 3 4.0 1.5 21.0in 3 6.0in 3 3.0 0.5

5. What is the maximum volume of the box according to this chart?

6. What happens if our increment gets smaller? What do we need to change? Is there a faster way to accomplish this?

7. Write the function and determine its domain.