53
Building polyhedra from their nets
Textbook: Part 2, lesson 53, pp. 64–65
GoalNets of polyhedra; making a cube and other bodies from a net.
New words
net · yoyilmafold line · buklash chizig‘iglue flap · yopishtirish tasmasicutting out · qirqish
Explanation
If we cut a body along its edges and flatten it, we get its net. Conversely, we can draw a net on paper, cut it out and fold it to make the body. The net of a cube consists of 6 squares, but not every arrangement of 6 squares folds into a cube. Folds are shown with dashed lines, and glue flaps are added to some squares. The net of a triangular prism has 2 triangles and 3 quadrilaterals; the net of a quadrilateral pyramid has 1 quadrilateral and 4 triangles. The net of a cylinder has 2 circles and 1 rectangle, and the net of a cone has 1 circle and 1 sector.
Worked examples
The net of a cube with edge 3 cm has area 6 · 3 · 3 = 54 cm² (6 squares). It equals the surface area of the cube.
The net of a pyramid with a square base of side 4 cm has 1 square and 4 equal triangles: 5 pieces, the same as the number of faces.
Class activity
“Making a cube”: on squared paper draw the net of a cube with edge 4 cm and add glue flaps. An adult should help with cutting with scissors; then fold and glue it.
Practice
1
Area (cm²) of the net of a cube with edge 5 cm?
150
2
How many pieces (shapes) are in the net of a triangular prism?
5
3
What shapes make up the net of a cylinder?
2 circles and 1 rectangle
4
Why do the squares of a cube's net match its faces?
A net shows all faces of the body in one plane; a cube has 6 square faces.