Question

There are two different ways to find surface area of a rectangular prism. One is by drawing the solid’s two-dimensional net and finding the area of each rectangular face. The other is by applying the formula for surface area of a prism. Both strategies can be used to work backwards and determine the dimensions of a rectangular prism with a given surface area.

In your post, describe the process you might use in order to determine the dimensions of a rectangular box to package a product, given a maximum surface area. In addition, elaborate on your journal post, sharing different possible box dimensions for a fixed surface area of 444 square inches.

Here are some other questions to consider for your post:

How can you minimize the number of calculations required to check whether your box is below the maximum surface area?
How can you use estimation skills to help you?
What is the relationship between the dimensions of your box and the volume it can contain? How can you maximize volume with a fixed surface area?
If the fixed surface area were a different number of square inches, would you have more possibilities for dimensions of your box?