Question

If 1300 square centimeters of material is available to make a box with a square base and an open top, find the largest possible

volume of the box.(include units)

Answer 1

4,096 cm^3

it's useful to know that the box with the largest volume - to - surface area ratio is a cube. Your shape will be a cube (with a missing top).

Thus there will be five square faces with a total area of 1300 square centimeters. The area of each side will thus be:

1300/5 = 260

The length of each side will again be an irrational number (√260), because 260 is not a perfect square. This comes out to roughly:

16

The simplest way to do it from here would be to simply take the cube of your side length:

163 = 4096

Your box's volume will be roughly 4096 cm^3