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Lowest common multiple and highest common factor

Square roots and cube roots

Writing indices and index laws

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Explainer Video

Tutor: Labib

Summary

Circles: Area and circumference

In a nutshell

All circles have a diameter and a radius. In combination with the Greek letter $\pi$ , these properties can be used to calculate the area and perimeter of a circle.

Diameter and radius

The diameter is a straight line from one side of a circle to another which passes through the centre. The radius is a straight line from the centre of a circle to its side.

The radius and diameter are linked by the formula:

$d = 2r$

Where $r$ is the radius of the circle, and $d$ is the diameter.

Example 1

What property of a circle is shown by the line $OA$ ?

Maths; Shapes; KS3 Year 7; Circles: Area and circumference

The line passes from the centre of a circle to a point on the side labelled $A$ .

This defines the radius.

The line OA is the radius of the circle.

Circumference of a circle

The circumference is the name given to the perimeter of the circle. The Greek letter $\pi$ is a constant ratio between the circumference of a circle and its diameter.

The circumference of a circle is given by:

$Circumference=2\pi r = \pi d$

$\pi \approx 3.142$

Note: The value of $\pi$ on a calculator can be used which will be more accurate.

Example 2

What is the circumference of a circle which has a radius of $3cm$ ? Leave your answer in terms of $\pi$ .

Use the radius to calculate the diameter.

$2 \times 3 = 6cm$

Multiply the diameter by $\pi$ .

$\underline{6 \times \pi = 6\pi \ cm}$

Note: Remember to maintain the units throughout the question.

Area of a circle

The area of circle is the size of its surface.

The area is given by the formula:

$\text{Area}=\pi r^2$

Example 3

The circle below has a radius of $5cm$ . What is the area in terms of $\pi$ ?

Identify the formula for the area of a circle.

${Area}=\pi r^2$

Use the formula to calculate the area.

${Area}=5^2 \times \pi$ 

$\underline{{Area}=25\pi \ cm^2 }$

Learn with Basics

Length:

Unit 1

2D shapes: Types and properties

Unit 2

Parts of a circle

Jump Ahead

Optional

Unit 3

Circles: Area and circumference

Final Test

Create an account to complete the exercises

FAQs - Frequently Asked Questions

What is the diameter of a circle?

The diameter is a straight line from one side of a circle to another which passes through the centre.

How do you calculate the area of a circle?

The formula for the area of a circle is πr^2, where r is the radius.

What is the circumference of a circle?

The circumference is the name given to the perimeter of the circle. The formula to calculate it is 2πr or πd, where r is the radius and d is the diameter.

Home

Maths

Shapes

Circles: Area and circumference

Videos

Summary

Exercises

Select Lesson

Statistics

Qualitative and quantitative data

Representing data: Graphs and charts

Mean, median, mode and range

Frequency tables

Averages from frequency tables

Averages from grouped frequency tables

Scatter graphs

Probability

Calculating probability

Equal and unequal probabilities

Relative frequency

Listing outcomes

Venn diagrams

Trigonometry

Pythagoras’ theorem

Trigonometric ratios: SOH CAH TOA

Finding missing lengths in a triangle

Finding missing angles in a triangle

Drawing shapes

Transformations

Constructions

Constructing triangles

Lines and angles

Types of angles

Angle rules

Interior and exterior angles

Parallel lines

Measures

Area and perimeter: Triangles and quadrilaterals

Area of compound shapes

Volume of prisms

Properties of shapes

Symmetrical shapes and rotational symmetry

Congruent shapes

Similar shapes

Nets and surface area

Shapes

Quadrilaterals: Types and properties

Triangles and regular polygons: Types and properties

Circles: Area and circumference

3D shapes: Identification and properties

Rates of change

Percentage change

Conversion factors

Imperial units

Solving best buy problems

Reading timetables

Maps and scale drawings

Speed: Formula and units

Density: Formula and units

Proportion

Ratio

Other graphs

Interpreting graphs

Solving simultaneous equations using graphs

Quadratic graphs

Travel graphs: Distance-time graphs

Conversion graphs

Straight line graphs

X and Y coordinates

Straight line graphs

Drawing straight line graphs

Finding the gradient

Equation of a straight line: y = mx + c

Drawing a graph of a linear equation

Estimating values using linear graphs

Formulae and equations

Substituting numbers into an expression

Writing and using formulae

Solving equations

Rearranging formulae

Number patterns and sequences

The nth term

Inequalities: Greater than or less than

Simultaneous equations

Algebraic manipulation

Algebraic notation

Algebraic terms

Simplifying algebraic expressions

Multiplying and dividing algebraic expressions

Single brackets: Expanding and factorising

Expanding double brackets: FOIL and multiplication grid

Fractions, decimals and percentages

Converting between fractions, decimals and percentages

Fractions

Fraction operations: Add, subtract, multiply, divide

Percentages

Rounding: Decimal places and significant figures

Rounding errors and estimating

Number calculations

Ordering numbers: Whole numbers and decimals

Addition and subtraction using the column method

Multiplying and dividing by powers of 10

Adding and subtracting decimals

Methods for multiplication and division

Order of operations: BIDMAS

Types of numbers

Understanding place value

Negative numbers: Add, subtract, multiply, divide

Special types of numbers

Multiples, factors and prime factors

Lowest common multiple and highest common factor

Square roots and cube roots

Writing indices and index laws

Standard form

Explainer Video

Tutor: Labib

Summary

Circles: Area and circumference

In a nutshell

All circles have a diameter and a radius. In combination with the Greek letter $\pi$ , these properties can be used to calculate the area and perimeter of a circle.

Diameter and radius

The diameter is a straight line from one side of a circle to another which passes through the centre. The radius is a straight line from the centre of a circle to its side.

The radius and diameter are linked by the formula:

$d = 2r$

Where $r$ is the radius of the circle, and $d$ is the diameter.

Example 1

What property of a circle is shown by the line $OA$ ?

The line passes from the centre of a circle to a point on the side labelled $A$ .

This defines the radius.

The line OA is the radius of the circle.

Circumference of a circle

The circumference is the name given to the perimeter of the circle. The Greek letter $\pi$ is a constant ratio between the circumference of a circle and its diameter.

The circumference of a circle is given by:

$Circumference=2\pi r = \pi d$

$\pi \approx 3.142$

Note: The value of $\pi$ on a calculator can be used which will be more accurate.

Example 2

What is the circumference of a circle which has a radius of $3cm$ ? Leave your answer in terms of $\pi$ .

Use the radius to calculate the diameter.

$2 \times 3 = 6cm$

Multiply the diameter by $\pi$ .

$\underline{6 \times \pi = 6\pi \ cm}$

Note: Remember to maintain the units throughout the question.

Area of a circle

The area of circle is the size of its surface.

The area is given by the formula:

$\text{Area}=\pi r^2$

Example 3

The circle below has a radius of $5cm$ . What is the area in terms of $\pi$ ?

Identify the formula for the area of a circle.

${Area}=\pi r^2$

Use the formula to calculate the area.

${Area}=5^2 \times \pi$ 

$\underline{{Area}=25\pi \ cm^2 }$

Learn with Basics

Length:

Unit 1

2D shapes: Types and properties

Unit 2

Parts of a circle

Jump Ahead

Optional

Unit 3

Circles: Area and circumference

Final Test

Create an account to complete the exercises

FAQs - Frequently Asked Questions

What is the diameter of a circle?

The diameter is a straight line from one side of a circle to another which passes through the centre.

How do you calculate the area of a circle?

The formula for the area of a circle is πr^2, where r is the radius.

What is the circumference of a circle?

The circumference is the name given to the perimeter of the circle. The formula to calculate it is 2πr or πd, where r is the radius and d is the diameter.