Nicholas,

A rectangular prism is the technical term for what most of us call a box shape. (See prism in our online glossary.)

Think of a cube, which is a rectangular prism, that is made of a specific amount (volume) of wet clay. Using flat tools and your hands you can flatten it into an oblong box like a case for a flute. Or flatten it even more into the shape of a pizza box, also a rectangular prism. In fact, you could flatten it to a molecule-thick pizza box, and it would be very large.

We didn't change the amount of clay, so the volume is the same. But is the surface area the same for all these rectangular prisms?

Cheers,
Stephen La Rocque.