**Maximize the volume of the lidless box formed from a 5 x 8 sheet with
a square removed from each corner.**

I used EXCEL to make a spreadsheet to do all the calculations and draw a graph. The first column represents the x which is the amount cut from one corner.

The second column is the length, calculated by subtracting 2x from 8. Similarly, the width is calculated by subtracting 2x from 5 and the height is the value of x.

Click **here** to see the GSP sketch.
You can drag the "Big Guy" point to change the value of x.

As you can see, the volume is maximized at x = 1, l = 6, w = 3, and h = 1. The volume is 18. Continuing the spreadsheet down, the values will get negative because you begin taking out more of a side than is actually there.

Looking at the picture we see another way of looking at the maximum.

The curve shows us once again that the maximum volume is when x = 1 which is where the curve reaches its maximum.