3D shapes
Shapes and nets
In this unit you learn to describe compound 3D shapes and to sketch nets for cubes, cuboids, prisms and pyramids. A net is a flat shape that folds up to make a 3D shape.
Compound 3D shapes
A simple shape is a single 3D shape, such as a cube, cuboid, prism or pyramid. A compound shape is made by joining two or more simple shapes together. To describe one, split it into the simple shapes you know. Some compound shapes can be split in more than one way — for example, the same shape might be a cube and a cuboid, OR two cuboids.
Faces of shapes
• A cube has 6 faces, all squares. • A cuboid has 6 faces (rectangles, and sometimes some squares). • A triangular prism has 5 faces: 2 triangles and 3 rectangles. • A square-based pyramid has 5 faces: 4 triangles and 1 square. A prism has two identical end faces plus one rectangle for each side of that end shape.
Nets
A net is a flat (2D) shape that folds up to make a 3D shape. The net of a closed cube is made of 6 squares; an open cube (a box with no lid) needs only 5 squares. There is more than one net for each shape, but you only need to sketch one of them.
Surface area
The surface area of a 3D shape is the total area of all its faces added together. Because a cube has 6 equal square faces, its surface area is 6 × the area of one face.
Worked examples
Describing a compound shape
- Look at the compound shape and think how to split it into simpler shapes you know.
- One way is a cube joined to a cuboid.
- Another way is two cuboids joined together.
Answer: The compound shape is a cube and a cuboid, OR two cuboids.
Describing the net of a cuboid
- A cuboid has six faces.
- In this cuboid four of the faces are rectangles and two are squares.
- The net is made of those 6 faces laid out flat so they fold up into the cuboid.
Answer: The cuboid's net has 6 faces: 4 rectangles and 2 squares.
Faces of a triangular prism
- Count the faces of a triangular prism.
- Two of the faces are triangles.
- Three of the faces are rectangles.
Answer: A triangular prism has 5 faces: 2 triangles and 3 rectangles.
Faces of a square-based pyramid
- Count the faces of a square-based pyramid.
- Four of the faces are triangles.
- One of the faces is a square (the base).
Answer: A square-based pyramid has 5 faces: 4 triangles and 1 square.
Surface area of a cube
- A cube has 6 equal square faces.
- Here each square face has an area of 4 cm².
- Add all the faces: surface area = 6 × 4.
Answer: The surface area of the cube is 6 × 4 = 24 cm².
Where you see this in real life
- Designing a gift box to hold chocolates by sketching its net first.
- Working in a factory that makes cuboid, cube, prism or pyramid boxes.
- Cutting out a net on paper and folding it to check the box is the right shape.
Key words
- Compound shape
- A 3D shape made by joining two or more simple shapes together.
- Net
- A flat shape that folds up to make a 3D shape.
- Face
- A flat surface of a 3D shape.
- Prism
- A 3D shape with two identical end faces and rectangles joining them.
- Surface area
- The total area of all the faces of a 3D shape.