Maths
What are 3D shapes?
Quick answer
3D shapes are solid shapes with length, width and height, like cubes, spheres, cylinders and pyramids. They have faces, edges and vertices.
In one sentence
A 3D shape is a solid object that takes up space, with length, width and height.
Explained
"3D" means three-dimensional. A sheet of paper is close to 2D, but a box has depth too, so you can hold it, stack it and fill it. Mathematicians describe 3D shapes using three words:
- Faces: the flat (or curved) surfaces.
- Edges: the lines where two faces meet.
- Vertices: the corners, where edges meet (one corner is a vertex).
box
ball
tent
| Shape | Faces | Edges | Vertices | Real-life example |
|---|---|---|---|---|
| Cube | 6 | 12 | 8 | dice |
| Cuboid | 6 | 12 | 8 | cereal box |
| Square-based pyramid | 5 | 8 | 5 | the pyramids at Giza |
| Triangular prism | 5 | 9 | 6 | ridge tent, a wedge of cheese |
| Cylinder | 3 (2 flat, 1 curved) | 2 | 0 | tin can |
| Cone | 2 (1 flat, 1 curved) | 1 | 1 | ice cream cone |
| Sphere | 1 curved | 0 | 0 | ball |
The faces of a 3D shape are 2D shapes. A cube's faces are squares; a triangular prism has two triangles and three rectangles.
A prism has the same shape all the way through, like a stick of rock: cut it anywhere parallel to the end and you see the same shape. A pyramid has a base and triangular faces that meet at a point.
Here is a neat fact for shapes with flat faces and no holes. Add the faces and vertices, then subtract the edges, and you always get 2. For a cube: 6 + 8 − 12 = 2. This is Euler's formula, named after the Swiss mathematician Leonhard Euler.
If you unfold a cardboard box flat, you get its net: the 2D pattern that folds up into the 3D shape. A cube has 11 different nets.
Examples
- A dice is a cube: 6 faces, 12 edges, 8 vertices.
- A ridge tent is a triangular prism.
- A football is (close to) a sphere.
- A traffic cone is a cone.
- Check Euler's formula on a triangular prism: 5 + 6 − 9 = 2.
Common mistakes
- Using 2D names for 3D shapes: a ball is a sphere, not a circle; a dice is a cube, not a square.
- Missing hidden edges and vertices at the back. Fix: hold a real object, or count edges in sets (top, bottom, sides).
- Mixing up cubes and cuboids. All the edges of a cube are the same length.
Quick quiz
3D shapes
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Question 1 of 4
How many faces does a cube have?
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Related topics
2D shapes
2D shapes are flat shapes with length and width but no thickness, like circles, triangles, squares and hexagons. You can draw them on paper.
Volume
Volume is the amount of space a 3D object takes up, measured in cubic units like cm³ or m³. A box 4 cm by 3 cm by 2 cm has a volume of 24 cm³.
Angles
An angle measures the amount of turn between two lines that meet at a point. Angles are measured in degrees (°); a right angle is 90° and a full turn is 360°.
Area
Area is the amount of flat space inside a shape, measured in square units like cm² or m². A rectangle 4 cm by 3 cm has an area of 4 × 3 = 12 cm².
Symmetry
A shape has symmetry when one half is a mirror image of the other (line symmetry), or when it looks the same after being turned (rotational symmetry).
Addition
Addition is putting amounts together to find a total. The sign is +, and the answer is called the sum or total, so 4 + 3 = 7.