Recognising 3D Shapes | mathismaths.com

What you will learn

Name a cube, cuboid, sphere, cylinder, cone and square-based pyramid.
Count the faces, edges and vertices of a solid shape.
Match real objects to their shapes, and sort shapes by whether they roll, stack or both.

Before you start: you should know that flat shapes such as squares and circles can be drawn on paper. Shapes All Around gives a first look at both flat and solid shapes. This lesson goes deeper into solids.

The idea

You cannot pick up a drawing of a circle, but you can pick up a ball. A 3D shape, also called a solid shape, takes up space. It has length, width and height. Flat shapes have just length and width.

Every object you handle is a 3D shape, or a mix of them. A dice, a drum, a party hat and a football are all different 3D shapes. This lesson helps you spot them, name them and tell them apart by counting.

The parts of a solid

Three words describe the parts of a solid shape.

A face is one surface. It can be flat or curved.
An edge is where two faces meet.
A vertex is a corner, where edges meet. More than one are called vertices.

Hold a box in your hand. The flat sides you can put your palm on are faces. The lines you can run a finger along, where two sides meet, are edges. The pointy corners are vertices.

Shapes with flat faces

These shapes have only flat faces, so they have straight edges and sharp corners.

Three solids with flat faces. A cube has 6 square faces. A cuboid has 6 rectangle faces. A square-based pyramid has 1 square face and 4 triangle faces. Dashed lines are edges hidden at the back.

A cube has six faces that are all the same square. A dice is a cube.
A cuboid has six rectangle faces, and faces on opposite sides match. A cereal box and a brick are cuboids.
A square-based pyramid has a square at the bottom and four triangles that meet at a point at the top.

A cube is a special cuboid, in the same way that a square is a special rectangle.

Shapes with curved faces

These shapes have at least one curved face, so some of them roll.

Three solids with curved faces. A sphere is all curved surface. A cylinder has two flat circles and a curved side. A cone has one flat circle, one curved side and a point.

A sphere is perfectly round. A football and a marble are spheres.
A cylinder has two flat circles joined by a curved side. A tin of soup and a drinking glass are cylinders.
A cone has one flat circle at the bottom and a curved side that goes up to a point. A party hat is a cone.

Shapes in everyday objects

Real objects are often not perfect shapes, but you can still say which shape they are closest to.

Everyday objects sorted by shape. Each column is a different solid. Many things you hold fit a column.

Roll, stack or both

How a shape behaves depends on its faces. Curved faces roll. Flat faces let a shape sit still and let other things sit on top of it.

A sphere rolls but cannot be stacked. A cube, cuboid and pyramid stack but do not roll. A cylinder does both, depending on how you put it down.

Worked examples

Example 1: Name the shape

A birthday hat has one flat circle at the bottom and ends in a point at the top. What shape is it? How many vertices does it have?

One flat circle, a curved side and a point: this is a cone.
The point at the top is the only corner.

Answer: A cone, with $1$ vertex.

Example 2: Count the parts

Count the faces, edges and vertices of a cuboid-shaped shoe box.

Faces: top, bottom, front, back, left and right. That is $6$ .
Edges: $4$ around the top, $4$ around the bottom and $4$ standing up. That is $4 + 4 + 4 = 12$ .
Vertices: $4$ on the top and $4$ on the bottom. That is $8$ .

Answer: $6$ faces, $12$ edges and $8$ vertices.

Example 3: Choosing a shape for a job

A shop wants to pile tins into a tall stack. Why is a cylinder good for this, and why would a sphere be a poor choice?

A cylinder has two flat circles, so one tin can sit on top of another.
A sphere has no flat face, so a sphere on top of a sphere rolls off.
A cylinder can also roll, so the shop needs to stack tins on their flat circles.

Answer: A cylinder has flat faces to stack on. A sphere has none, so it rolls away.

A shape can look different from different sides. A cuboid stood on its end looks tall and thin, but it is the same cuboid. Check its faces, edges and vertices, not just the way it is sitting.

Why it matters

Knowing 3D shapes helps you choose the right container, pack a bag and build things. Boxes are cuboids because they stack and fill space well, and balls are spheres because they roll. Architects use cubes and pyramids, and engineers use cylinders for pipes and wheels. Later, you will find the surface area and volume of these same shapes, so it helps to know their faces and edges now.