Connect 3D objects to their nets
In Year 4 (NSW Stage 2, outcome MA2-3DS-01), students learn to connect 3D objects to their nets. A net is a flat pattern that folds up to make a solid, and each flat piece is one face of the object, so the number of pieces always matches the number of faces.
This topic covers the nets of a cube, a rectangular prism, a cylinder, a cone, a square pyramid, a triangular pyramid and other prisms, and how to match a solid to its net by counting squares, rectangles, triangles and circles. These skills help Stage 2 students picture and describe the shapes they see every day.
Theory
Connecting 3D objects to their nets is a Year 4 space skill: a net is a flat pattern that folds up to make a solid, and each flat piece is one face. This page explains how to match solids to their nets and count faces, with the nets of a cube, cylinder, square pyramid and prisms.
A 3D object is a solid you can hold, like a box, a can or a dice. A net is what you get when you unfold that solid and lay it out flat. Each flat shape in the net is one face of the object.
Because every face becomes one flat piece, the number of pieces in the net matches the number of faces (a curved surface counts as one piece too). A cube has 6 square faces, so its net is 6 equal squares. A cylinder has a top, a bottom and a curved side, so its net is 2 circles and 1 rectangle. A cone has a flat circle and a curved side, so its net is 1 circle and 1 fan shape.
To match a solid to its net, count each kind of face on the solid, then check the net has exactly the same pieces. If the shapes or the counts do not match, the net will not fold into that object.
Nets do not need a formula, but this table pins the net of each common solid. The number of pieces is always the same as the number of faces, counting a curved surface as one piece.
| Solid | Faces | Net is made of |
|---|---|---|
| Cube | 6 | 6 squares |
| Rectangular prism | 6 | 6 rectangles |
| Square pyramid | 5 | 1 square, 4 triangles |
| Triangular prism | 5 | 2 triangles, 3 rectangles |
| Triangular pyramid | 4 | 4 triangles |
| Cylinder | 2 flat, 1 curved | 2 circles, 1 rectangle |
| Cone | 1 flat, 1 curved | 1 circle, 1 fan shape |
How to match a solid to its net
- Name the faces. Look at the solid and name every face, including any hidden at the back, such as the top and bottom of a can.
- Count each kind. Count how many squares, rectangles, triangles or circles the solid has.
- Check the net. The net must have the same shapes in the same numbers, joined so they can fold up (6 squares in one long row cannot). Then the net folds into the solid.
| rectangles | \(=\) | \(6\) |
| 6 rectangle faces | \(\to\) | rectangular prism |
The net folds into a rectangular prism, a box shape.
| \(\text{pieces}\) | \(=\) | \(4\text{ triangles}\) |
| \(\text{faces}\) | \(=\) | \(4\) |
The three outside triangles fold up around the middle one and meet at a point. It makes a triangular pyramid with \(4\) faces.
| \(\text{square pyramid}\) | \(=\) | \(1\text{ square} + 4\text{ triangles}\) |
| \(4 - 3\) | \(=\) | \(1\) |
She needs 1 more triangle, joined to the empty side of the square (the dashed outline).
| \(\text{pieces}\) | \(=\) | \(2 + 5 = 7\) |
| \(\text{each piece}\) | \(=\) | \(1\text{ face}\) |
The solid has \(7\) faces. It is a pentagonal prism, with a pentagon at each end.
Common pitfalls
Frequently asked questions
What is a net in maths?
A net is a flat pattern made from the faces of a 3D object. When you fold the net up along the joins, it makes the solid.
Is there only one net of a cube?
No. There are 11 different nets of a cube. Each one is 6 equal squares, but not every way of joining 6 squares works: 6 squares in one long row will not fold into a cube.
Why does the net of a cylinder have a rectangle?
The curved side of a cylinder unrolls into a flat rectangle, like the label peeled off a tin. The circles are the flat top and bottom.
How do you match a 3D object to its net?
Count each kind of face on the solid, then check the net has the same pieces. A triangular pyramid has 4 triangular faces, so its net must be 4 triangles.
Do the pieces of a net have to be joined?
Yes. A net is one piece, with the faces joined along their sides. When you fold it up, each join becomes an edge of the solid.
Does the number of net pieces equal the number of faces?
Yes. Each flat piece in the net becomes one face when the solid is folded up, so the number of pieces is the same as the number of faces. A curved surface, like the side of a cylinder, is one piece too.