We know you're tired of surface area. You should be. Not only have we been harping on it for the past four chapters, we've only scraped the surface (area?) of the third dimension.
We took a look at 3D shapes, but found areas and circumferences and heights, all two-dimensional concepts that we already know. There's a whole other aspect to the third dimension that's been hidden from us. Like we've been living in the Matrix this whole time.
Don't worry. We're about to unplug from it. Wave goodbye to surface areas and distances, and say hello to volume.
Unlike Pantene commercials and Metallica concerts, volume isn't about big hair or torn eardrums. Volume is about the amount of space that a figure encloses. It's about units cubed instead of squared. It's about thinking inside the box. Or boxes.
Instead of calculating how much wrapping paper it takes to cover the outside of a gift box, we now have to think about what's inside it. A sweater vest? Three thousand jellybeans? A Toyota Prius? It all depends on volume.