1. Week 10 Perimeter, area and volume (including circles)
Functional MATHS
Week 10
Perimeter, area and volume (including circles)

2. What are the arrows for A to M pointing to?
Today’s starter…
What are the arrows for A to M pointing to? A B C D E F G H I J K L M

3. Units and measures What did we do last week?
Estimate, measure and compare length, capacity and weight
Convert between metric units
Convert between metric and imperial units (L2)
Solve problems requiring calculation with temperature, time and money

4. Units and measures
Recap

5. What units do we measure the following in?
Length
Weight
Capacity (volume)

6. Metric Conversions - LENGTH
Functional Skills Mathematics - Measurements
Metric Conversions - LENGTH

7. How many metres to London?
Units of Distance
1km = 1000 m 1 m = 100 cm 1 cm = 10 mm
Use these relationships to help you work out the following problems:
London 5 km
How many metres to London?
5 000 m
Km to m

8. 0.95 km Units of Distance 1km = 1000 m 1 m = 100 cm 1 cm = 10 mm
Use these relationships to help you work out the following problems:
How many km to Berlin?
Centre 950 m
0.95 km

9. Units of Distance 2.15 m length 215 cm 0.9 m width = 90 cm
1km = 1000 m 1 m = 100 cm 1 cm = 10 mm
Use these relationships to help you work out the following problems:
Find the length and width of the pool table in cm.
2.15 m
length 215 cm
0.9 m
width = 90 cm

10. Units of Distance height = 7650 mm width = 3040 mm
1km = 1000 m 1 m = 100 cm 1 cm = 10 mm
Use these relationships to help you work out the following problems:
Find the height and width of the tower in mm.
height = 7650 mm
7.65 m
width = mm
3.04 m

11. Metric Conversions - Weight
Functional Skills Mathematics - Measurements
Metric Conversions - Weight

12. Units of weight This German shepherd puppy weighs 5.4kg.
What is this in grams?
5.4 x 1000 =
5400 grams

13. Metric Conversions – Capacity (volume)
Functional Skills Mathematics - Measurements
Metric Conversions – Capacity (volume)

14. Units of capacity (volume)
The liquid in this jug is filled to 300ml.
300 / 1000 =
0.3 litres
What’s this in litres?

15. Write these down and work them out…
You need to be able to convert distances between mm, cm, m, km
50cm = m
3000m = km
500mm = cm
6.5m = cm
1.5m = mm
0.5 3 50
650
1500

16. Task: Organising the new office
How many filing cabinets are you able to fit along the wall with the desk?
How much space is there left along the wall

17. Put your name on it please before handing in!
Directed Study

18. What are we going to do today?
Perimeter, area and volume
Use metric units in everyday situations
Work out areas and perimeters in practical situations
Find the area, perimeter and volume of common shapes (including circles)
Please write your SMART target on the top of your blue feedback form …

19. Perimeter

20. Perimeter 15 m 5 m 5 m 15 m Perimeter = 15 m + 5 m + 15 m + 5 m = 40 m
The perimeter of a shape is the distance around the outside.
Rectangles
15 m
5 m
5 m
Length
Width
15 m
Perimeter =
15 m
+ 5 m
+ 15 m
+ 5 m
= 40 m

21. Example
4 cm
7 cm
Essential working
Perimeter = = 22 cm
Perimeter = = 22 cm
Perimeter = 2 x 11 = 22 cm
Perimeter = 2 x x 7 = 22 cm
Discuss these different ways of showing your method. Can you think of any others?

22. Find the perimeter of each rectangular shape below.1 2 3 4 5
8½ cm
5½ cm
90 feet
50 feet
210 cm
90 cm
Not to scale.
280 ft
300 m
600 cm = ?
320 m
28 cm

23. Find the perimeter of the shapes below.
5 cm
Find the perimeter of the shapes below.
Regular Pentagon
Regular Hexagon
Regular Quadrilateral
6 cm
7 cm
Irregular Quadrilateral
3 mm
4 mm
6 mm
9 mm
7 mm
10 mm
Irregular Pentagon
Diagrams not to scale
Square
P= 4 x 5 = 20 cm
P= 5 x 6 = 30 cm
P= 6 x 7 = 42 cm
P= = 16 mm
P= = 32 mm

24. Perimeter of Compound Shapes
Diagrams Not to scale
Perimeter = ? 1m 3m 4m
4 m +
4 m +
7 m +
3m +
3m +
1m +
= 22m

25. Perimeter of Compound Shapes
Not to scale
Perimeter = ?
5 m
4 m
2 m +
2 m +
5 m +
4 m +
2 m +
2 m +
5 m +
8 m
= 30 m

26. Area

27. 18 cm2 AREA 6 cm 3 cm 1 cm2 Area = 6 cm x 3 cm = 18 cm2
Remember: The perimeter of a shape is a measure of distance around the outside.
The area of a shape is a measure of the surface/space contained within its perimeter.
Area is measured in units2
Units of distance mm cm m km
inches
feet
yards
miles
Units of area
mm2
cm2 m2
km2
inches2
feet2
yards2
miles2
1 cm
1 cm2
6 cm
3 cm
Metric
Imperial
18 cm2
Area = 6 cm x 3 cm = 18 cm2

28. Find the area of each rectangular shapes below.
100 m
50 m
120 m
40 m 1 2 3 4 5
8½ cm
5½ cm
90 feet
50 feet
210 cm
90 cm
Not to scale.
4500 ft2
5 000 m2
cm2
4 800 m2
46.75 cm2

29. Area of Compound Shapes
Diagrams Not to scale
Area of Compound Shapes
16 m2
9 m2
Area = 4 x x 3 = = 25 m2

30. 6 cm
2 cm
8 cm
12 cm
4 cm
6 cm
2 cm
8 cm
12 cm
4 cm
8 cm2
12 cm2
16 cm2
24 cm2
2 cm
8 cm2
12 cm2
2 cm
Area = = 40 cm2
Area = = 40 cm2

31. Area of Compound Shapes
Not to scale
16 m2 ?
6 m2
3 m
20 m2 ?
4 m
Area = = 42 m2

32. Perimeter and Area Exercise
New Flat:
Perimeter and Area Exercise
Plan of flat
Plan of garden

33. Volume

34. Front face 20 cm2 2D Volume of a Cuboid 3D 4 cm 5 cm
Remember: the area of a shape is a measure of the surface/space contained within its perimeter. 2D
Volume of a Cuboid
The volume of a shape is a measure of the space contained within its faces/boundary. 3D
1 cm
1 cm3
1 cm2
1 cm
Units of area
mm2
cm2 m2
km2
inches2
feet2
yards2
miles2
Metric
Imperial
Units of volume
mm3
cm3 m3
km3
inches3
feet3
yards3
miles3
Metric
Imperial
4 cm
Front face
20 cm2
5 cm

35. 20 cm3 40 cm3 60 cm3 2D 3D Volume Volume of a Cuboid 5 cm 4 cm 3 cm
Remember the area of a shape is a measure of the surface/space contained within its perimeter.
Units of area
mm2
cm2 m2
km2
inches2
feet2
yards2
miles2
Metric
Imperial
1 cm2
1 cm
The volume of a shape is a measure of the space contained within its boundary.
Units of volume
mm3
cm3 m3
km3
inches3
feet3
yards3
miles3
1 cm3
5 cm
4 cm
20 cm3
40 cm3
60 cm3
3 cm
Volume = 4 cm x 5 cm x 3 cm = 60 cm3

36. Volume of a Cuboid
9.6 mm
5 mm
2.3 mm
Find the volume of the following cuboids (to 1 dp)
Diagrams not to scale.
12 cm
8.1 cm
1.3 cm
3.1 cm 1 2 3
Volume = 2.3 x 9.6 x 5 = mm3
Volume = 3.1 x 3.1 x 3.1 = cm3
Volume = 1.3 x 12 x 8.1 = cm3

37. Volume of Objects 6 cm 3 cm 21 cm 13 cm 1.1 m 1.3 m 1.8 m
Volume = 3 cm x 13 cm x 21 cm = 819 cm3
Volume = 63 = 216 cm3
Volume = 1.3 m x 1.8 m x 1.1m = 2.574m3

38. Volume of Compound Shapes
8 cm
12 cm
5 cm
2 cm
3 cm
Not to scale
Volume = 5 x 2 x 8= 80 cm3
80 cm3
512 cm3
288 cm3
Volume = 83 = 512 cm3
Volume = 12 x 3 x 8= 288 cm3
Volume = = 880 cm3

39. Volume problems worksheet

40. Volume problems worksheet

41. Volume problems worksheet

42. Circles
Circumference
Area

43. circumference. radius. The distance all the way round the outside
of a circle is called the
circumference.
Radius
From the centre of
the circle to the
circumference is
called the
radius.

44. diameter diameter A line which passes through
the centre of a circle and
touches the circumference
twice is called a
diameter
diameter

45. r = ½ D D = 2r The radius is half of the diameter radius radius

46. Pi to the first 1000 decimal places is:-
Even with all these decimal places -
pi still works out to be a bit more than 3

47. Area of a circle =
 x the radius squared
A =  r 2

48. Circumference of a circle =
 x the diameter
C =  D

49. Circumference and area of a semi circle??
Just half it!
÷ by 2

50. The circumference of a Circle
C =  D
Find the circumference of the following circles. 1 2
8 cm
18.7 cm
C =  D
C =  x 16
C = 50.3 cm (1 dp)
C =  D
C =  x 18.7
C = 58.8 cm (1 dp)

51. The Area of a Circle A = r2 1 2
Find the area of the following circles. 1 2
8 cm
9.5 cm
A = r2
A =  x 82
A = cm2 (1 dp)
A = r2
A =  x 9.52
A = cm2 (1 dp)

52. A = r2 Find the area of the clock face and radar screen. 12 cm 60 cm
A =  x 122
A = cm2 (1 dp)
A = r2
A =  x 302
A = 2827 cm2 (nearest cm2)

53. The Area of a Circle A = r2 1 2
Find the area of the following semi-circles. 1 2
8 cm
9.5 cm
A = ½r2
= ½ x  x 42
= 25.1 cm2 (1 dp)
A = ½r2
= ½ x  x 4.752
= 35.4 cm2 (1 dp)

54. Directed Study

55. Please complete and bring back next week….
Level 1
Level 2