Solid Shapes

Describe cubes, cuboids, prisms, pyramids, cylinders, cones and spheres by counting their faces, edges and vertices.

About 3 min read
  • Name common 3D solids
  • Count the faces, edges and vertices of a solid
  • Match a solid to its net
Before you start

You already know 2D shapes such as squares, rectangles, triangles and circles. Solids are built from these shapes.

What makes a shape solid?

A flat shape has length and width. A solid has length, width and height, so it takes up space. A box, a tin of beans and a football are all solids. To describe a solid exactly, we count three things instead of relying on how it looks.

Definition: face

A flat or curved surface of a solid.

Definition: edge

A line where two faces meet.

Definition: vertex

A corner where edges meet. The plural is vertices.

Common solids

| Solid | Faces | Edges | Vertices | | --- | --- | --- | --- | | Cube | 6 | 12 | 8 | | Cuboid | 6 | 12 | 8 | | Triangular prism | 5 | 9 | 6 | | Square-based pyramid | 5 | 8 | 5 |

A cylinder has 2 flat faces and 1 curved face. A cone has 1 flat face, 1 curved face and a point called the apex. A sphere has 1 curved face and no edges.

Nets

A net is a flat shape that folds up to make a solid. A cube's net is made of 6 squares. Every face of the solid appears exactly once in its net, so counting the faces is a quick way to check a net.

Describe a triangular prism

A tent has the shape of a triangular prism. How many faces, edges and vertices does it have?

The two ends are triangles, which gives 2 faces. The sides are 3 rectangles, so there are 5 faces.

Each triangle has 3 edges, and 3 more edges join the triangles, so there are 9 edges.

Each triangle has 3 corners, so there are 6 vertices.

Answer: 5 faces, 9 edges and 6 vertices.

Faces are not only flat

A cylinder has curved surfaces as well as flat ones. Count the curved surface as a face, and say that it is curved.

Exam focus
Say it like this“A cube has 6 faces, 12 edges and 8 vertices.”
Not like this“A cube has 6 sides and 8 points.” — Use the exact words faces, edges and vertices.
Common mistakeCounting only the faces you can see in the drawing and forgetting the hidden ones.

Practice

How many faces does a cuboid have?
6 faces, in 3 matching pairs.
How many vertices does a square-based pyramid have?
5 vertices: 4 around the base and 1 at the top.
Which solid has 1 flat face, 1 curved face and an apex?
A cone.
Going further
A net has 2 triangles and 3 rectangles. Which solid does it make?
A triangular prism. The triangles are the ends and the rectangles join them.

Quick check

Solid shapes quick check

How many edges does a cube have?

There are 4 edges on the top, 4 on the bottom and 4 joining them.

Which solid has no edges and no vertices?

Its only surface is curved, so no two faces meet to form a line or corner.

How many squares are in the net of a cube?

A net shows every face exactly once, and a cube has that many square faces.
Key takeaways
  • Solids have length, width and height.
  • Describe a solid by its faces, edges and vertices.
  • A net is a flat shape that folds into a solid.
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