Hello, realintegerz!

If 12,000 cm² of material is available to make a box

with a square base and an open top, find the volume of the box

as a function of the width of the base of the box. Code:

*-------*
/| /|
/ | / |
*-------* |
| | |
| | |
h| | *
| | /
| |/ x
*-------*
x

Let = side of the square base.

Let = height of the box.

The panels comprising the box is made up of:

. . a base with area

. . and four sides with area each.

The total surface area is: .

We are told that the total surface area will be 12,000 cm².

So we have: . .[1]

The volume of the box is: .

Substitute [1]: .