The link above will take you to several problems involving volume from the Open Middle website – a great collection of non-routine problems. Many of these problems involve maximizing the volume of various shapes given different constraints. Several of them involve surface are and volume together. As with all Open Middle problems, these have hint questions teachers can ask students who are stuck.

Here’s an example: What is the least amount and greatest amount of surface area possible on a rectangular prism with a volume of 64 cubic inches? (Use whole numbers only)