Geometry and measures - Properties and constructions: identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres

The idea

A face is a flat surface, an edge is where two faces meet, and a vertex is where edges meet. A cube has six square faces, twelve edges and eight vertices; a cuboid has the same counts with rectangular faces. A prism has the same cross-section all along its length, with two identical end faces and rectangles joining them, so a triangular prism has five faces, nine edges and six vertices. A pyramid has a base with triangular faces meeting at an apex, so a square-based pyramid has five faces, eight edges and five vertices. A cylinder has two flat circular faces, one curved surface, two circular edges and no vertices. A cone has one flat circular face, one curved surface, one circular edge and one vertex at the apex. A sphere has one curved surface, no flat faces, no edges and no vertices. Questions ask you to count these, to name a solid from its properties, or to match a solid to its net.

What earns the marks

• The correct count of faces, edges or vertices for a named solid, including zero counts where they apply.
• Naming the solid correctly from its properties or from its net.
• Identifying the cross-section of a prism.
• A clear reason when asked why a solid is or is not a prism.
• Stating the edge and vertex properties of curved solids, such as a cylinder's two circular edges and no vertices, a cone's one circular edge and one apex-vertex, and a sphere's zero edges and vertices.

Common mistakes and how to put them right

• Leaving out the hidden edges and vertices that the drawing shows as dashed lines.

• Calling the curved surface of a cylinder a face, when a face is flat.

• Treating a cylinder as a prism when the question asks for a solid whose cross-section is a polygon.

• Miscounting the edges of a pyramid by forgetting the edges of the base.

• Giving a sphere or cylinder vertices when it has none, or omitting the circular edges of a cylinder or cone.

Exam tips

• Count the faces in groups, the top, then the bottom, then the sides, so that none is missed.
• On a solid with flat faces only, such as a prism or a pyramid, check your counts by adding the faces to the vertices, which should come to two more than the number of edges.
• For curved solids, decide separately whether each boundary is a flat face, a curved surface, an edge or a vertex, and record zero counts explicitly.