Creative
Thinker
Effective
Participator
Independent
Enquirer
Reflective
Learner
BRAIN IN GEAR
PLT Skills
Self Manager
Team
Worker
Which ones are you using?
EXAMPLE
DITDIONA can be rearranged to make ADDITION
TASK
Work out the following Mathematical anagrams:
REPRMEITE
Perimeter
SADRIU
Radius
AIDETERM
Diameter
EXTENSION
Develop your own Mathematical anagrams as above as a
creative thinker.
Creative
Thinker
Effective
Participator
Independent
Enquirer
Reflective
Learner
Self Manager
Team
Worker
AREA OF CIRCLES AND SEMI-CIRCLES
TASK
MATCH THE
CARDS AT
THE
BOTTOM
WITH THE
EMPTY
BOXES
TANGENT
CHORD
SECTOR
DIAMETER
SEGMENT
RADIUS
CIRCUMFERENCE
Creative
Thinker
Effective
Participator
Independent
Enquirer
Reflective
Learner
Self Manager
Team
Worker
PLT Skills NAMING CIRCLE PARTS ANSWERS Which ones are you using?
RADIUS
SECTOR
DIAMETER
CIRCUMFERENCE
SEGMENT
TANGENT
CHORD
Creative
Thinker
PLT Skills
Effective
Participator
Independent
Enquirer
Reflective
Learner
AREA OF CIRCLES AND SEMI-CIRCLES
Self Manager
Which ones are you using?
radius
EXAMPLES
(a)Find the area of the circle:
(b) Find the area of the circle:
4cm
14m
diameter
Area of circle = 3.14 x 4 x 4
Area of circle = 50.2cm 2 (1d.p.)
Area of circle = 3.14 x 7 x 7
Area of circle = 153.9 m2 (1d.p.)
(c)Find the area of the semi-circle:
Area of semi-circle =
Area of semi-circle =
20cm
2
2
Area of semi-circle = 157cm 2
Team
Worker
Creative
Thinker
Effective
Participator
Independent
Enquirer
Reflective
Learner
Self Manager
Team
Worker
PLT Skills AREA OF CIRCLES AND SEMI-CIRCLES Which ones are you using?
TASK (GRADE D)
EXTENSION (GRADE C)
1) Calculate the area of the circles below:
(a)
(b)
(c)
1) Calculate the area of the semi-circles
below:
(b)
(a)
2cm
1.5cm
6cm
13cm
9cm
2)Calculate the area of the circles below:
(a)
(b)
(d)
(c)
(c)
3cm
8cm
20cm
7cm
3) Find the area of one face of the following
coins. Give your answers to 1 decimal
place.
a) 1p coin, radius 1 cm
b) 2p coin, radius 1.3 cm
c) 5p coin, diameter 1.7 cm
d) 10p coin, diameter 2.4 cm
12cm
2) Calculate the area of the quadrant
below:
PLENARY ACTIVITY
EXAM STYLE QUESTION (GRADE C)
Calculate the area shaded black.
Area of big circle = 3.14 x 5 x 5
Area of small circle = 3.14 x 3 x 3
Area of big circle = 78.5cm 2
Area of small circle = 28.26cm 2
Area shaded black = 78.5 - 28.26 = 50.2 cm 2 (1d.p.)
Creative
Thinker
Effective
Participator
Independent
Enquirer
Reflective
Learner
BRAIN IN GEAR
PLT Skills
Self Manager
Team
Worker
Which ones are you using?
EXAMPLE
DITDIONA can be rearranged to make ADDITION
TASK
Work out the following Mathematical anagrams:
OCHDR
Chord
TAGTENN
Tangent
CAR
Arc
EXTENSION
Develop your own Mathematical anagrams as above as a
creative thinker.
Creative
Thinker
Effective
Participator
Independent
Enquirer
Reflective
Learner
NAMING CIRCLE PARTS
PLT Skills
TASK
Self Manager
Team
Worker
Which ones are you using?
MATCH THE
CARDS AT
THE
BOTTOM
WITH THE
EMPTY
BOXES
TANGENT
CHORD
SECTOR
DIAMETER
SEGMENT
RADIUS
CIRCUMFERENCE
Creative
Thinker
Effective
Participator
Independent
Enquirer
Reflective
Learner
Self Manager
Team
Worker
PLT Skills CIRCUMFERENCE OF CIRCLES Which ones are you using?
diameter
EXAMPLES
(a)Find the circumference of the circle:
8cm
(b)Find the circumference of the circle:
11m
radius
Circumference of a circle = 3.14 x 8
Circumference of a circle = 25.1cm (1d.p.)
Circumference of a circle = 3.14 x 22
Circumference of a circle = 69.1m(1d.p.)
Creative
Thinker
Effective
Participator
Independent
Enquirer
Reflective
Learner
Self Manager
Team
Worker
PLT Skills CIRCUMFERENCE OF CIRCLES Which ones are you using?
TASK (GRADE D)
EXTENSION (GRADE C)
1) Calculate the circumference of the circles:
(a)
(b)
1) Find the perimeter of the semi-circles:
(c)
(b)
(a)
3cm
8.5cm
7cm
15cm
9cm
2)Calculate the circumference of the circles:
(a)
(b)
(d)
(c)
(c)
3cm
2cm
6cm
2.5cm
3) Find the circumference of one face of the
following coins. Give your answers to one
decimal place.
a) 1p coin, diameter 2 cm
b) 2p coin, diameter 6 cm
c) 5p coin, radius 0.85 cm
d) 10p coin, radius 1.2 cm
12cm
2) Calculate the perimeter of the quadrant
below:
PLENARY ACTIVITY
FUNCTIONAL MATHS QUESTION (GRADE D)
The diagram represents a race track on a school playing field. The diameter of
each circle is shown.
In a race with four runners, each runner starts and finishes on the same inner
circle of their lane after completing one circuit.
How much further than A does D have to run?
Extra Distance =
Circumference of A = 3.14 x 60
Circumference of A = 188.4 m
Circumference of D = 3.14 x 66
Circumference of D = 207.24 m
207.24m – 188.4m
Extra Distance =
18.8m(1d.p.)
Finding the Area of a Sector
The general formula for finding the area is:
Area of sector= Angle of Sector x πr2
360
Fraction of full
circle that sector
covers
“of”
Area of full
circle
Finding the Area of a Sector
Sometimes it is not easy to see what fraction of a full circle you have.
You can work it out based on the size of the angle. If a full circle is 360°
, and this sector is 216°, the sector is 216/360, which can be simplified
to 3/5.
For Example-
The sector here is 3/5 of a full circle
Find the area of the full circle
216°
7cm
Area= π x 72
= π x 49
= 153.93804
= DON’T ROUND YET!
Then find 3/5 of that area
3/5 of 153.93804 = 92.362824 (divide
by 5 and multiply by 3)
= 92.4cm2
Sometimes the fraction cannot be simplified and will stay over 360
Questions
Find the area of these sectors, to 1 decimal place
1
3
2
10cm
11cm
260°
190°
4
12cm
251°
6
5
87°
ANSWERS
5cm
6.5cm
32°
1
2
3
4
5
6
226.9
200.6
315.4
19.0
61.2
80.7
17cm
166°
HOME
Finding the Perimeter of a Sector
To find the perimeter of a sector, you need to work out what fraction of a full
circle you have, then work out the circumference of the full circle and find the
fraction of that circumference.
You then need to add on the radius twice, as so far you have worked out the length
of the curved edge
For Example-
The sector here is ¾ of a full circle
Find the area of the full circle
7cm
Area= π x 14 (the diameter is twice the radius)
= 43.982297......
= DON’T ROUND YET!
Then find ¾ of that circumference
¾ of 43.982297...... = 32.99 cm (2 dp)
Remember to add on 7 twice from the straight
sides
Finding the Perimeter of a Sector
The general formula for finding the area is:
Perimeter of sector= (Angle of Sector x πd) + r + r
360
Fraction of full circle
that sector covers
“of”
Circumference of full
circle
Don’t forget the
straight sides
This is the same as d
of 2r, but I like r +r as
it helps me
remember why we
do it
Finding the circumference of a Sector
Sometimes you will not be able to see easily what fraction of the full
circle you have.
To find the fraction you put the angle of the sector over 360
250°
This sector is 250/360 or two
hundred and fifty, three
hundred and sixty-ITHS of
the full circle
Simplify if you can
Sometimes the fraction cannot be simplified and will stay over 360
Questions
Find the perimeter of these sectors, to 1 decimal place
1
3
2
10cm
11cm
260°
190°
4
251°
6
5
87°
12cm
5cm
6.5cm
32°
ANSWERS
1
65.4
2
58.5
3
76.6
4
17.6
5
31.8
6
43.5
17cm
166°
HOME
Compound Area and Perimeter
Here we will look at shapes made up of triangles, rectangles, semi and quarter circle
Find the area of the shape below:
10cm
8cm
10cm
Area of this
rectangle= 8
x10
=80cm2
Area of this semi circle = π
r2 ÷ 2
= π x 52 ÷ 2
= π x 25 ÷ 2
=39.3 cm2 (1dp)
Area of whole shape = 80 +
39.3
= 119.3
cm2
Compound Area and Perimeter
Find the perimeter of the shape below:
10cm
8cm
10cm
Perimeter of this
rectangle= 8 + 8 +
10
=26cm
(don’t include the
red side)
Circumference of this semi circle =
πd ÷ 2
= π x 10 ÷ 2
=15.7 cm (1dp)
Perimeter of whole shape =
26 + 15.7
= 31.7 cm
Compound Area and Perimeter
Find the areaof the shape below:
Area of this quarter circle = π r2 ÷ 4
= π x 52 ÷ 4
= π x 25 ÷ 4
=19.7 cm2 (1dp)
5cm
10cm
11cm
Area of this rectangle
10 x 11=110
Area of whole shape = 110+
19.7
= 129.7cm2
Compound Area and Perimeter
Work out all
Find the perimeter of the shape below:
missing sides first
?
Circumference of this quarter circle = πd ÷ 4
= π x 10 ÷ 4 (if radius is 5, diameter is
10)
=7.9 cm (1dp)
5cm
5cm
6cm
10cm
10cm
11cm
Add all the straight
sides=
10+10 + 11+ 5 + 6=
42cm
Area of whole shape = 42+ 7.9
= 49.9cm
Questions
ANSWERS
AREA PERIMETER
1 38.1
23.4
21
135.0
61.3
Find the perimeter and area of these shapes, to
decimal place
3 181.1
60.8
2cm
3 4 27.3
1
2
12cm
10cm
5
129.3
47.7
20cm
6 128.5
6cm
11cm
4cm
17cm
4cm
4
Do not worry about
perimeter here
5cm
12cm
6
6cm
5
Do not worry about
perimeter here
10cm
5cm
10cm
5cm
20cm
HOME
Area of Segments
Here we will look at finding the area of sectors
You will need to be able to do two things:
1) Find the area of a sector using the
formula-
2) Find the area of a triangle using
the formulaArea= ½ absinC
Area of sector= Angle of Sector x πr2
360
a
C
b
Examplefind the area of the blue segment
Step 1- find the area of the whole secto
Area= 100/360 x π x r2
= 100/360 x π x 102
=100/360 x π x 100
=87.3cm2
10cm
10cm
100°
Step 2- find the area of the triangle
Area= ½ absinC
=1/2 x 10 x 10 x sin100
= 49.2cm2
Step 3- take the area of the triangle
from the area of the segment
87.3 – 49.3 = 38 cm2
Examplefind the area of the blue segment
Step 1- find the area of the whole secto
Area= 120/360 x π x r2
= 120/360 x π x 122
=120/360 x π x 144
=150.8cm2
12cm
12cm
120°
Step 2- find the area of the triangle
Area= ½ absinC
=1/2 x 12 x 12 x sin120
= 62.4cm2
Step 3- take the area of the triangle
from the area of the segment
150.8 – 62.4 = 88.4 cm2
Questions
1
ANSWERS
1 75.1
2 29.5
3 201.1
Find the area of the blue segments, to 1 decimal place
4 8.3
3
2
5 51.8
10cm
6 33.0
85° 11cm
170° 12cm
130°
4
6
5
6.5cm
95°
5cm
160°
65°
17cm
HOME
Finding the Radius or angle of a Sector
r
100°
10cm
Area=200cm2
x
Area= 100 x π x
r2
360
200= 100 x π x r2
360
Area=150
Area= θ x π x r2
360
150= θ x π x 102
360
200x360 = r2
100 x π
150x360 = θ
102 x π
229.2=r2
15.1cm =r
117.9°= θ
Questions
ANSWERS
1 7.6
2 8.3
Find the missing radii and angles of these sectors, to 1 decimal 3place
5.4
4 160.4
3
1
2
5 122.1
r
r
r
6 47.6
200°
175°
Area=100cm
2
4
250°
Area=120cm
2
6
5
5cm
θ
Area=35cm2
6.5cm
θ
Area=45cm2
Area=50cm2
17cm
θ
Area=120cm
2
HOME