Identify properties of the faces, surfaces, edges and vertices of: cubes,…

The idea

Identify properties of 3D shapes by counting faces, surfaces, edges and vertices. A face is a flat surface; a curved surface is distinct. An edge is where surfaces meet, and a vertex is a corner. A cube has 6 square faces, 12 edges and 8 vertices. A cuboid shares these counts but has rectangular faces. A prism has a constant cross-section, with identical polygonal ends and rectangular sides. A cylinder has two circular faces, one curved surface, two circular edges and no vertices. A pyramid has a polygonal base and triangular faces meeting at an apex. A cone has one circular face, one curved surface, one vertex and one circular edge. A sphere has one curved surface, no edges and no vertices. Recall these properties for each solid.

What earns the marks

• Distinguishes between flat faces and curved surfaces when describing a 3D shape.
• States the number and shape of faces for cubes, cuboids, prisms, cylinders, pyramids, cones and spheres.
• Identifies edges as line segments or curves where surfaces meet, and counts them correctly for the named shapes.
• Identifies vertices as corners where edges meet, and recognises that cylinders and spheres have none.
• Recognises that a prism has a uniform cross-section and that its side faces are rectangles.
• Recognises that a pyramid has triangular faces meeting at a single apex above a polygonal base.
• Applies these properties to classify an unfamiliar 3D shape or to complete a table of properties.

Common mistakes and how to put them right

• Calling the curved surface of a cylinder or cone a face.

  Put it right by using the term curved surface and reserving face for flat surfaces.

• Saying a cylinder has vertices because it has circular edges.

  Put it right by noting that a vertex is a point where edges meet, and a cylinder has no such points.

• Confusing a prism with a pyramid.

  Put it right: A prism has a constant cross-section and rectangular side faces, while a pyramid has triangular faces meeting at an apex.

• Counting the same edge or vertex twice when a shape is drawn in a tilted orientation.

  Put it right by marking each edge or vertex as you count it.

• Thinking a sphere has one face because it looks round.

  Put it right by describing it as having one curved surface, no edges and no vertices.

Exam tips

• Read the options carefully and eliminate any that confuse faces with curved surfaces.
• For a named shape, recall the standard counts first, then check them against the diagram if one is given.
• If a shape is unfamiliar, decide whether it has a constant cross-section (prism) or an apex (pyramid) before counting.
• Use precise vocabulary: face, edge, vertex, curved surface, cross-section, apex.