Circumference of a Circle

Parts of a circle

Calculate d from r Calculate r from d

Introducing pi

Using C =π d

C from d …. 5 circles

C given radius

5 questions

C from r …. 5 circles

5 questions

C given radius or diameter ( 5 circles)

5 questions

Distance round a window

Circumference

Learning IntentionLearning IntentionTo identify the main parts of a circle.To identify the main parts of a circle.

Success CriteriaSuccess Criteria

1.1. Know the terms circumference, Know the terms circumference, diameter and radius.diameter and radius.

2.2. Identify them on a circle.Identify them on a circle.3.3. Calculate the circumference using Calculate the circumference using

formula.formula.

Main Parts of a circle

O

Circumference

C ir

c

u

m

fere

n

c

e

The curved distance around the edge of a circle is called the curcumference

O marks the centre of the circle

ALL the points on the circumference are the same distance from the centre

A line from the centre to the circumference is called the radius

The diameter of a circle splits the circle in two

radi

us

diameter

The diameter is the largest distance between two points on the circumference. The diameter passes through the centre of the circle

Know Radius. Find Diameter

3cm

0

1 2 3

4 5 6

7 8 9

C

.

÷

x

0

+

On

²

-

Ans

=

√

(-)

The dashed line is also a radius of the circle

3 cm

6cm

The diameter of a circle is twice its radius.

Diameter = 2 x 3cm = 6cm

19.7cm

Radius = cm

Diameter =

= cm

Next

Know Diameter. Find Radius

3cm

0

1 2 3

4 5 6

7 8 9

C

.

÷

x

0

+

On

²

-

Ans

=

√

(-)

3 cm

6cm

The radius is half the diameter

Radius = Diameter ÷ 2

Radius = 6 ÷ 2 = 3 cm

18.

8cm Diameter

=cm

Radius = = cm

Next

Circumference of a circle

The Greek mathematician Archimedes of Syracuse (287- 212 BC) who flourished in Sicily is generally considered to be the greatest mathematician of ancient times

O

Diameter

He is credited with determining the relationship between the the circumference of a circle andits diameter

Circumference

No matter the size of the circle the CIRCUMFERENCE of the circle is roughly 3 times its DIAMETER

CIRCUMFERENCE = 3 x DIAMETER

More Accuracy

3.141592653589793238462643383279502…

Maths experts for years have been trying to get a more accurate answer to …. circumference ÷ diameter

circumference ÷ diameter is roughly

There isn’t an exact answer for this. It actually goes on forever!

We’ll stop here since it would stretch for 600

miles if we printed them all!

In 1989 a computer worked it out to 480 million decimal places.

3

CIRCUMFERENCE = 3 x DIAMETER means that

More Accuracy

We can use a ruler to measure the diameter.

How can we measure the circumference?

Measuring Circumference

Measure length of label …or

…….. by rolling

Roll along an even surface Be careful to avoid slip!

Starting pointEnd point

Checking it out

Construct a table shown below to enable usto record our results.

Circle Circumference = C Diameter = D C+D= C- D= C/D= CxD=

1

2

3

4

5

6

7

8

Circle I nvestigation Calculations

The previous slides demonstrated ways of measuring the diameter and the circumference

Your answer should be close to 3

Another approach

3 8 15

C ÷ d

C ÷ d

Sides

2.6

5.20

3.06

3.31

3.12

3.19

Draw polygons inside a circle

and outside a circle

As the number of sides increase the shapes look more like a circleDivide the perimeter of polygon by the diameter of circle

Answers approach the value of 3.14

Using Polygons

Ancient Greeks were experts in drawing and manipulating shapes

They would know how to draw regular polygons accurately

Instead of using decimals they would use fractions

Instead of using decimals they would use fractions

One value he reached in his calculations was22

722

7= 22 ÷ 7 = 3.142857……..

The figures on the previous slide were determined using a computer

…. C ÷ d ….. by computer

3.141592653589793238462643383279502…

There isn’t an exact answer

We’ll stop here since it would stretch for 600

miles if we printed them all!

In 1989 a computer worked it out to 480 million decimal places.

It actually goes on forever!

More accurate measurement

If it goes on for ever how can I write it down?

We use the Greek letter

instead.

MathematicalGenius!

This is called pi.

The Circumference

When doing circle calculations on the calculator use

=3.14

x diameter C

= d

C = 3.14 x d

Circumference =

C = 3 x diameter

C =π x diameter

Rough answers C =3.141592653589……. x diameter

Accurate Answer

Circumference of a Circle

C =π d

18.

8cm

Next 0 1 2 3 4

5 6 7 8 9

C

.

÷x

0+

On

²

-

Ans

=

√(-)

C =

x

C =

π d

3.14

18.8

C from d

5.4

18.2

14.416.

8

0 1 2 3 4

5 6 7 8 93.14x

C

.

÷x

0+ On

²

-

Ans

=

√(-)

9.6

Next Five

π

A C

3.14

Diameter

r=

d=

r=

d=

r=

d=

r=

d=

r=

d=

Circumference of a Circle from Diameter

C =π d

Next

d = 3.4

d = 7.2

d = 14.6

d = 13.2

d = 8.6

C =π d

C =π d

C =π d

C =π d

=

=

=

=

=

=

=

=

=

=

0 1 2 3 4

5 6 7 8 9

C

.

÷x

0+ On

²

-

Ans

=

√(-) 3.14

Circumference of a Circle

C =π d

8.6

cm

Next

C = C =

Diameter=

=

Radius=

0 1 2 3 4

5 6 7 8 9

C

.

÷x

0+ On

²

-

Ans

=

√(-) π3.14

Calculate diameter 1st

C from r

8.69.4

6.2

2.3

0 1 2 3 4

5 6 7 8 9

C

.

÷x

0+ On

²

-

Ans

=

√(-)

5.1

Next Five

π

A C

3.14

Radius

r=

d=

r=

d=

r=

d=

r=

d=

r=

d=

==

=

=

=

Circumference of a Circle from r

C =π d

Next 0 1 2 3 4

5 6 7 8 9

C

.

÷x

0+ On

²

-

Ans

=

√(-)

r = 6.2

r = 4.7

r = 3.5

r = 8.3

r = 7.6

C =π d

C =π d

C =π d

C =π d

=

=

=

=

=

=

=

=

=

=

3.14

C from d or r

7.38.7

2.510.

8

0 1 2 3 4

5 6 7 8 9

C

.

÷x

0+ On

²

-

Ans

=

√(-)

19

Next Five

π

A C

3.14

r OR d

r=

d=

r=

d=

r=

d=

r=

d=

r=

d=

Circumference of a Circle r or d

C =π d

Next 0 1 2 3 4

5 6 7 8 9

C

.

÷x

0+ On

²

-

Ans

=

√(-)

d = 9.4

r = 3.4

d = 12.8

r = 8.2

d = 3

C =π d

C =π d

C =π d

C =π d

=

=

=

=

=

3.14 x 9.4

3.14 x 3

29.516

9.42

=

=

=

=

=

Perimeter of Circular Window

40 cm

60

cm

Perimeter is round the edge

Know the following sides

60

cm

?

No rule for this but ……

C =π d

C =3.14 x

40

40

C =125.6 ÷

2D =125.6÷2

D =62.8

Perimeter =

60

+ 40

+ 60

+ 62.8 = 222.8

Find the Perimeter

Four Semicircles round a square of side 14 cm

The four semicircles can be made into TWO circles

C= π

0

1 2 3

4 5 6

7 8 9

9x6

C

.

÷

x

54

+

On

²

-

Ans

=

√

(-)

0 1 2 3 4

5 6 7 8 9

C

.

÷x

0+ On

²

-

Ans

=

√(-)