Volume and Surface Area of a Box

Where it usually goes wrong

Volume and surface area get treated as one measure of how big a box is, so making a box “bigger” is assumed to make both bigger together. They do not keep step: three boxes can hold exactly the same amount and need quite different amounts of card to wrap.

Try this

• Press Long, Flat and A cube in turn. Each holds the same, and the wrapping figure changes every time.
• Find the shape that needs the least card for what it holds. It is the cube, and that is why so many things are packed in near-cubes.
• Stretch one edge and watch both numbers. Doubling an edge doubles what it holds and does something quite different to the skin.

Where this goes next

This is why a small animal loses heat faster than a large one, and why a box of anything costs what it costs to ship.