Inside and outside a box
How much a box holds and how much card it takes to wrap are two different measurements. Stretch the box and they stop keeping step.
Holds 4 × 3 × 3 = 36 Takes to wrap 2 × (12 + 12 + 9) = 66
- The three edges
- 4, 3 and 3
Drag the ring at the end of any edge to resize the box.
Three boxes that hold eight
Ready to try some? Volume worksheets, or surface area and nets
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.