Mathematics

Problem

An open-top box with a square base is to be made from material that provides a total surface area of

192\text{ cm}^2

(including the base but not a lid). Let

x

be the length of a side of the base and

h

the height. What is the height of the box that maximizes its volume? a)

6\text{ cm}

4\text{ cm}

2\text{ cm}

8\text{ cm}