Geometry
3D shapes
You see 3D shapes all around you. In this section you will name and describe spheres, cubes, cuboids, cylinders, cones and pyramids, and count their faces and vertices.
Faces and vertices
A face is a flat surface of a 3D shape. A vertex is a corner. 'Vertices' means more than one corner. A curved surface, like the outside of a ball, does not count as a face.
Cubes and cuboids
A cube has 6 square faces and 8 vertices. A cuboid also has 6 faces and 8 vertices, but its faces are rectangles, not all squares. A box is often a cuboid.
Spheres, cylinders and cones
A sphere (like a ball) is round all over. It has no flat faces and no vertices, and it can roll. A cylinder (like a tin) has 2 flat circle faces and a curved surface. A cone has 1 flat circle face and a point at the top (a vertex).
Pyramids
A square-based pyramid has a square bottom and 4 triangle faces that meet at a point. That is 5 faces and 5 vertices.
Worked examples
Naming a cube
- Look at a 3D shape with flat square faces.
- Count the faces: there are 6, and each is a square.
Answer: A shape with 6 square faces is a cube.
Faces of a cuboid
- Look at a box shape.
- Count the flat surfaces on the outside.
Answer: A cuboid has 6 faces.
Vertices of a cube
- A vertex is a corner.
- Count the corners of a cube.
Answer: A cube has 8 vertices.
A shape that rolls
- Look for a shape that is round all over with no flat faces.
- A curved surface lets it roll.
Answer: A sphere can roll and has 0 vertices.
Where you see this in real life
- A dice is a cube.
- A tin of beans is a cylinder.
- An ice-cream cone is a cone, and a ball is a sphere.
Key words
- Face
- A flat surface of a 3D shape.
- Vertex
- A corner of a shape. More than one is called vertices.
- Curved surface
- A rounded surface, like the outside of a ball. It does not count as a face.
- Cube
- A 3D shape with 6 square faces and 8 vertices.
- Sphere
- A round 3D shape, like a ball, with no faces or vertices.