# Maximizing the Volume of an Open Top Box

The total surface area of a square based open-top rectangular box is 12 cm^2.

Find the dimensions of the box of maximum volume.

https://brainmass.com/math/geometry-and-topology/maximizing-the-volume-of-an-open-top-box-166773

#### Solution Preview

Suppose the base of the box is x cm and the height is y cm.

Then the total surface area of the open box has four sides and one base. Each side ...

#### Solution Summary

The volume of a box is maximized using derivatives.

$2.19