What it shows
Stacking identical boxes shows that volume is repeated cubic units, while joining them hides some faces and reduces the total surface area. It is also a useful desk organiser.
The science
Volume of a cuboid is length times breadth times height, and the surface area is the sum of the areas of all six faces. When you glue two boxes face to face, two faces disappear from the outside, so the surface area is less than twice that of one box, while the volume doubles. This is the reason big animals lose heat more slowly than small ones, and how packing saves wrapping paper.
Materials
Cost: free. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- 12 empty matchbox trays and sleeves
- Glue or double-sided tape
- Coloured paper to cover the outside
- Small beads as drawer knobs
- A ruler
- A notebook
Safety
For this project: Use only empty matchboxes with no matches inside. An adult must remove any leftover heads and strikers.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
Step by step
8 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Measure the length, breadth and height of one matchbox in centimetres and write them down.
Calculate its volume and surface area using the formulas.
Glue three sleeves in a row, then four rows on top of each other to form a block of 12 (3 by 4).
Calculate the volume and the visible surface area of the block and compare to twelve separate boxes.
Cover the outside with coloured paper to fit the surface area you calculated.
Add bead knobs to the drawers and test they slide.
Fill the drawers with paper clips, pins and erasers.
Fill a table: one box, 2, 4, 12 boxes with volume and surface area and spot the pattern.
What you should see
A working drawer block whose table shows that the volume grows with the number of boxes faster than the surface area.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
01What is the formula for volume of a cuboid?
Length times breadth times height.
02Why does the surface area not double when two boxes join?
The two joined faces are hidden inside.
03How many faces does a cuboid have?
Six.
04How did you check your paper covering?
By comparing the paper area used with the calculated surface area.
Take it further
Rearrange 12 boxes into 2 by 3 by 2 and 1 by 3 by 4 and find which shape needs the least wrapping paper.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
Free ebooks for this project
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