Home

Maths

Shapes and area

3D shapes: faces, edges, vertices

3D shapes: faces, edges, vertices

Videos

Summary

Exercises

Select Lesson

Exam Board

Select an option

Statistics

Sets and Venn diagrams
Sampling and bias
Collecting data: types and classes of data
Mean, median, mode and range
Simple charts and graphs
Pie charts
Scatter graphs
Frequency tables: finding averages
Grouped frequency tables
Box plots - Higher
Cumulative frequency - Higher
Histograms and frequency density - Higher
Interpreting data
Comparing data sets

Probability

Basics of probability
Calculating theoretical probabilities
Probability: Expected and relative frequency
The AND / OR rules
Probability tree diagrams
Conditional probability - Higher
Experimental probability: frequency trees

Trigonometry

Pythagoras' theorem
Sin, cos, tan
Trigonometry: Finding angles and sides
Exact trigonometric values
Sine and cosine rules - Higher
3D Pythagoras - Higher
3D Trigonometry - Higher
Vectors
Vectors - Higher

Angles and geometry

Angles: types, notation and measuring
Basic angle rules
Angles in parallel lines
Circle theorems - Higher
Constructing triangles: SSS, SAS, ASA
Construction: angle and perpendicular bisectors
Construction: Loci
Bearings
Maps and scale drawings

Shapes and area

Properties of 2D shapes
Congruence: conditions for congruent triangles
Similar shapes: Scaling
The four transformations
Area and perimeter: Formulae
Area and circumference of circles: Formulae
3D shapes: faces, edges, vertices
Surface area of 3D shapes: Nets, formulae
Volume of 3D shapes: Formulae
Volume of 3D shapes: Comparing, rates of flow
Area and volume scale factors
Projections and elevations of 3D shapes

Ratio proportion and rates of change

Ratio
Direct and inverse proportion
Finding percentages and percentage change
Compound growth and decay
Converting units: metric and imperial
Converting units: area and volume
Time intervals: converting units of time
Speed, density and pressure: Formulae and units

Graphs

Coordinates and midpoints
Straight line graphs
Drawing straight line graphs
Finding the gradient of a straight line
Equation of a straight line: y = mx + c
Coordinates and ratio
Parallel and perpendicular lines
Quadratic graphs
Reciprocal and cubic graphs
Exponential graphs and circles - Higher
Trigonometric graphs - Higher
Solving equations using graphs
Graph transformations - Higher
Real-life graphs
Distance-time graphs
Velocity-time graphs - Higher
Gradients of real-life graphs - Higher

Algebra

Simplifying algebraic expressions
Multiplying and dividing algebraic expressions
Single brackets: Expanding and factorising
Double brackets: Expanding and factorising
Double and triple brackets - Higher
Solving equations
Expressions, equations, formulae, functions and identities
Writing formulae and equations from word problems
Writing formulae and equations from diagrams
Rearranging formulae
Factorising quadratics
The quadratic formula - Higher
Complete the square - Higher
Algebraic fractions - Higher
Sequences
Finding the nth term
Solving inequalities
Inequalities on graphs - Higher
Iteration - Higher
Simultaneous equations: elimination and substitution
Non-linear simultaneous equations - Higher
Algebraic proof - Higher
Composite and inverse functions - Higher

Number

Types of numbers
Order of operations: BODMAS
Multiplying and dividing by powers of 10
Multiplying and dividing whole numbers
Multiplying and dividing decimals
Negative numbers: add, subtract, multiply, divide
Prime numbers and prime factorisation
Multiples, factors and prime factors
LCM and HCF
Fractions
Fractions, decimals and percentages
Writing recurring decimals as fractions
Rounding: Integers, decimal places, significant figures
Estimation
Error intervals
Upper and lower bounds - Higher
Powers and roots: Square and cube numbers
Laws of indices: multiply, divide, brackets
Index laws: negative and fractional indices - Higher
Surds: Simplify, add and subtract - Higher
Rationalising surds - Higher
Standard form calculations

Explainer Video

Loading...
Tutor: Bilal

Summary

3D shapes: faces, edges, vertices

In a nutshell

There are eight main 3D shapes that you need to learn. 3D shapes also have their own parts that can be labelled such as faces, edges and vertices.



Names of common 3D shapes

Here are a list of 3D shapes you need to know.


name

illustration

Cube
Maths; Shapes and area; KS4 Year 10; 3D shapes: faces, edges, vertices

Cuboid
Maths; Shapes and area; KS4 Year 10; 3D shapes: faces, edges, vertices

Sphere
Maths; Shapes and area; KS4 Year 10; 3D shapes: faces, edges, vertices

Cylinder
Maths; Shapes and area; KS4 Year 10; 3D shapes: faces, edges, vertices

Square-based pyramid
Maths; Shapes and area; KS4 Year 10; 3D shapes: faces, edges, vertices

Triangular-based pyramid (also known as a tetrahedron)
Maths; Shapes and area; KS4 Year 10; 3D shapes: faces, edges, vertices

Cone
Maths; Shapes and area; KS4 Year 10; 3D shapes: faces, edges, vertices

Triangular prism
Maths; Shapes and area; KS4 Year 10; 3D shapes: faces, edges, vertices



Labelling 3D shapes

There are three important terms to know when dealing with 3D shapes.


name

Definition

Face

A flat (2D) surface on the 3D shape

Edge

A line where two faces meet

Vertex

A point where two or more edges meet

​

Example 1

How many faces, edges and vertices does a cube have?


By drawing a transparent cube, it can be seen that a cube has:


  • 666​ faces
  • ​121212​ edges
  • ​888​ vertices
Maths; Shapes and area; KS4 Year 10; 3D shapes: faces, edges, vertices



Read more

Exercises

Easy

5 Exercises

Medium

5 Exercises

Hard

4 Exercises

Create an account to complete the exercises

Basics

3D shapes: Identification and properties
3D shapes: Identification and properties

Overview

Learning Goals

    Overview

    FAQs - Frequently Asked Questions

    What is the face of a 3D shape?

    A face of a 3D shape is a flat (2D) surface.

    What is an edge of a 3D shape?

    The edge of a 3D shape is a line where two faces meet.

    What is a vertex of a 3D shape?

    The vertex of a 3D shape is a point where 2 or more edges meet.

    ©2020 - 2024 evulpo AG

    Beta