Directions: What is the least and greatest amount of surface area possible on a rectangular prism with a volume of 64 cubic inches and whole number side lengths?

### Hint

### Hint

How do you find the Surface Area of a Rectangular Prism?

### Answer

### Answer

minimum: 96 cubic inches (4 x 4 x 4)

maximum: 258 cubic inches (1 x 1 x 64)

maximum: 258 cubic inches (1 x 1 x 64)

Source: Marie Isaac, Katrin Marti, and Ryan Turner

We have been working on volume in my high school equivalency class, but we haven’t discussed surface area yet. I scaffolded this problem by breaking it into two questions:

1) What are the dimensions of three different rectangular prisms that all have a volume of 64 square inches?

2) Which of your shapes from question #1 would take the most material to make?

It turned out that the students who showed up had enough thinking with just figuring out number 1. For one student who had missed a lot of class, we talked about the formula v=lwh and rewrote it as 64=_ x _ x _. Part 2 was a bit over their heads, so we worked it as a class by finding the area of the sides of each shape and adding them together. If class had been bigger today or if a different group had shown up, I think some of them could have figured it out on their own. I might try this again another day with a different. The students who were here today could still get more out of the problem.

* different volume