What it shows
A cube of side 5 cm hinged along its edges opens flat into a net of six 5 cm squares, so its surface area is 6 times 25 = 150 square cm. A second box, 5 by 4 by 3 cm, opens to show three pairs of rectangles with total area 94 square cm.
The science
Surface area is the total area of all the faces, which is the area of the net. A cube has six identical square faces, so its surface area is 6 times the side squared. A cuboid with edges l, b and h has three pairs of equal rectangles, so its surface area is 2 times (lb + bh + hl). Covering each face with grid paper lets you count the square centimetres directly and check the formula.
Materials
Cost: free. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- Thick chart paper or thin cardboard
- Cloth tape for hinges
- A ruler and pencil
- Centimetre grid paper glued on each face
- Scissors
Safety
For this project: An adult must help with cutting the cardboard.
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
7 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.
Cut six 5 cm squares of card and glue centimetre grid paper on one side of each.
Join them with tape hinges in a cross shape: four in a column and one on each side of the second square.
Fold the net up into a cube and tape a small tab so it stays closed, then open it flat again.
Count the small squares on the open net: 25 on each face, 150 in all.
Cut two 5 by 4, two 4 by 3 and two 5 by 3 rectangles, cover with grid paper and hinge them into a cuboid net.
Count or calculate: 2 times (20 + 12 + 15) = 94 square cm, and check by counting the grid.
Display both nets open and closed with the formulas, and show that eleven different nets fold into a cube.
What you should see
The cube net counts to 150 square cm and the 5 by 4 by 3 box to 94 square cm, matching 6 a squared and 2(lb + bh + hl).
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 surface area of a cube of side 10 cm?
600 square cm.
02How many different nets fold into a cube?
Eleven.
03How is surface area different from volume?
Surface area is the area of the outside faces, measured in square units; volume is the space inside, in cubic units.
04Which cuboid faces are equal?
Opposite faces: top and bottom, front and back, left and right.
Take it further
Leave one face off the cube to make an open box and show that it has only five faces, so its outside area is 125 square cm for side 5 cm.
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.
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