87
The net of a cube
Textbook: Part 3, lesson 87, pp. 58–60
GoalThe net of a cube is made of 6 equal squares; the total surface area is S = a × a × 6.
New words
net · yoyilmasquare · kvadrattotal surface · to‘la sirtface · yoq
Explanation
If we cut a cube along some edges and lay it flat we get its net. The net of a cube consists of 6 identical squares. But not every shape made of 6 squares folds into a cube: for example, 6 squares in one row do not. The total surface area of a cube is the sum of the areas of all its faces: S = a × a × 6.
Worked examples
Edge 5 cm: one face is 5 × 5 = 25 cm², the total surface is 25 × 6 = 150 cm².
Edge 4 dm: S = 4 × 4 × 6 = 96 dm².
Class activity
“Cut out the net”: on squared paper children draw a cube net, cut it out, fold and glue it, and colour one face.
Practice
1
A cube has edge 3 cm. What is the area of one face in cm²?
9
2
A cube has edge 8 cm. What is its total surface area in cm²?
384
3
How many cm² of paper are needed to wrap a cube-shaped box with edge 10 cm (ignore overlaps)?
600
4
The total surface of a cube is 216 cm². What is the area of one face in cm²?
36
5
A cube has edge 2 dm. What is its total surface area in cm²?
2400