Science:Math Exam Resources/Courses/MATH110/April 2016/Question 07/Hint 1

You want to maximize the volume of the box. Therefore, this is an optimization problem.

Write down an equation for the volume of the box in terms of the side length $\ell$ of the base, and the height $h$ of the box.

Then, write down an expression for the surface area of this box. There is a square base of side length $\ell$ and four rectangles making up the sides of the box. You know that the surface area should be equal to $1200$ square centimeters. You can use this to find a relationship between $\ell$ and $h$ to plug into your volume equation.