The properties of 3D shapes booklet
The properties of 3D shapes booklet
- Unit 1: Numbers
- Unit 2: Geometry and measure
- Unit 3 : Statistics and probability
🎯 In this topic you will
- Identify and describe the 2D faces of 3D shapes.
- Describe the properties of 3D shapes.
🧠 Key Words
- cone
- edge / edges
- face / faces
- prism
- pyramid
- vertex / vertices
Show Definitions
- cone: A 3D shape with one circular base and a curved surface that meets at a single point (the apex).
- edge / edges: A line segment where two faces of a 3D shape meet.
- face / faces: A flat (or sometimes curved) surface that makes up part of the outside of a 3D shape.
- prism: A 3D shape with two identical, parallel faces (bases) and side faces that join the bases.
- pyramid: A 3D shape with a polygon base and triangular faces that all meet at one point (the apex).
- vertex / vertices: A corner point where edges meet on a 2D or 3D shape.
🧩 Getting to Know 3D Shape Properties
This section will help you to become more familiar with the properties of 3D shapes. You will practise using the vocabulary you need to describe shapes. This will help you to talk about 3D shapes clearly with other people.
❓ EXERCISES
$1$. Copy and complete the sentences to show the number of triangular and rectangular faces.
a. A triangular prism has ____ rectangular faces and ____ triangular faces.
b. A cuboid has ____ rectangular faces and ____ triangular faces.
c. A square-based pyramid has ____ rectangular faces and ____ triangular faces.
d. A cone has ____ rectangular faces and ____ triangular faces.
👀 Show answer
a. A triangular prism has $3$ rectangular faces and $2$ triangular faces.
b. A cuboid has $6$ rectangular faces and $0$ triangular faces.
c. A square-based pyramid has $1$ rectangular face and $4$ triangular faces.
d. A cone has $0$ rectangular faces and $0$ triangular faces.
$2$. This is a pentagonal prism.
a. How many faces does it have?
b. What shape faces does it have?
👀 Show answer
a. It has $7$ faces.
b. It has $2$ pentagonal faces and $5$ rectangular faces.
$3$. A hexagonal pyramid has $7$ faces. Write the shape of each face.
👀 Show answer
It has $1$ hexagonal face (the base) and $6$ triangular faces.
$4$. This is a model of a square-based pyramid. Max has used straws to make the edges. He has used modelling clay to join the edges to the vertices.
a. How many straws has he used?
b. How many pieces of modelling clay has he used?
c. How many straws would Max need to make a model of a cuboid?
d. How many pieces of modelling clay would Max need to make a model of a cuboid?
👀 Show answer
a. A square-based pyramid has $8$ edges, so he used $8$ straws.
b. A square-based pyramid has $5$ vertices, so he used $5$ pieces of modelling clay.
c. A cuboid has $12$ edges, so Max would need $12$ straws.
d. A cuboid has $8$ vertices, so Max would need $8$ pieces of modelling clay.
🧠 Reasoning Tip
You could compare the faces, edges or vertices.
$5$.
a. Choose two of these shapes. Classify the shapes by writing a property that the shapes have in common.
b. Which of the shapes has at least one triangular face?
c. Which of the shapes has more than $6$ vertices?
d. Which of the shapes have fewer than $12$ edges?
👀 Show answer
a. Example: Choose A and C. They both have only rectangular faces.
b.B and E.
c.A, C and D.
d.B and E.
$6$. Describe this shape in sentences.
👀 Show answer
This is a prism. The front and back faces are the same step-shaped (L-shaped) face. The other faces are rectangles, and the edges meet at right angles.
$7$. Cubes are special types of cuboids.
a. If a cuboid is also a cube what is the fewest number of square faces it can have?
b. How many faces can it have that are not squares?
c. If a cuboid is not a cube what is the greatest number of square faces that it can have?
d. Write two sentences to describe how cubes and cuboids are similar and different.
👀 Show answer
a.$6$.
b.$0$.
c.$2$.
d. Cubes and cuboids both have $6$ faces, $12$ edges and $8$ vertices. A cube has all faces as equal squares, but a cuboid can have rectangular faces of different sizes.
🧠 Think like a Mathematician
Use up to $12$ straight straws and some modelling clay.
Tasks:
👀 show answer
Suggested findings for (a):
- $1$–$5$ straws: you cannot make a closed $3$D shape (you can only make open “frames” or flat shapes). A closed polyhedron needs enough edges to enclose a space (volume).
- $6$ straws: you can make a tetrahedron (triangular pyramid). This is the smallest standard polyhedron frame (it has $6$ edges).
- $8$ straws: you can make a square-based pyramid (it has $8$ edges).
- $9$ straws: you can make a triangular prism (it has $9$ edges).
- $10$ straws: you can make a pentagonal pyramid (it has $10$ edges).
- $12$ straws: you can make a cube/cuboid (it has $12$ edges) and also a hexagonal pyramid (it has $12$ edges).
Generalisation:
- Pyramids: an $n$-gon pyramid has $2n$ edges, so any even number of straws from $6$ upwards can make a pyramid frame (choose $n=\frac{E}{2}$).
- Prisms: an $n$-gon prism has $3n$ edges, so any multiple of$3$ from $9$ upwards can make a prism frame (choose $n=\frac{E}{3}$).
- Numbers that will not work (for these families):$1$–$5$ definitely cannot make a closed $3$D shape; and numbers that are neither$2n$ (with $n\ge 3$) nor$3n$ (with $n\ge 3$) will not make a prism or pyramid frame.
Help for (b): When you record your results, list each shape name and its straw count (for example: tetrahedron $6$, square-based pyramid $8$, triangular prism $9$, pentagonal pyramid $10$, cube/cuboid $12$).