1. MATHS
Week 10
More Measures

2. Starter!
You’ve heard of elf on a shelf – can you work out these maths rhymes?

9. What did we do last week?

10. Metric Conversion Quiz
10 quick questions on metric conversion
Write numbers 1 – 10 on a piece of paper and get ready ……….

11. There are 1000 of these in a kilogram
There are 100 of these in a metre
How many millilitres are there in a litre?
There are 1000 of these in a Tonne
There are 10 of these in a centimetre
There are 1000 metres in a ……..?
How many millilitres are there in 1 centilitre?
There are 1000 of these in a litre
There are 1000 of these in a metre
How many centilitres are there in a litre?

12. There are 1000 of these in a kilogram grams
There are 100 of these in a metre centimetre
How many millilitres are there in a litre? 1000
There are 1000 of these in a Tonne kilograms
There are 10 of these in a centimetre millimetres
There are 1000 metres in a ……..? kilometre
How many millilitres are there in 1 centilitre? 10
There are 1000 of these in a litre millilitres
There are 1000 of these in a metre millimetres
How many centilitres are there in a litre? 100

13. What are we going to do this week?
Recap Converting Metric Measures
Recap Converting Imperial to Metric
Perimeter, area and volume

14. Perimeter, area and volume

15. Two questions to have a go at:
Find the volume of this cuboid:
The tank below contains exactly 100 litres of water. How far up the tank does the water go? (Hint: 1 litre = 1000cm³)
8cm
6cm
0.5m
5cm
0.5m 1m
Answer: 240cm³
Answer: 0.2m or 20cm

16. Circles

17. Parts of a Circle
Centre

18. Parts of a Circle
Diameter (must go through the centre)

19. Parts of a Circle
Radius (half a diameter – from the outside to the centre)

20. d = 2r or r = d/2 Radius and Diameter
The radius is half of the diameter OR
The diameter is double the radius
d = 2r or r = d/2

21. Parts of a Circle
Sector (like a slice of pizza)

22. Parts of a Circle
Chord (a line that crosses the circle but not through the centre)

23. Parts of a Circle
Segment (looks a bit like an orange segment)

24. Parts of a Circle
Circumference (the perimeter of the circle)

25. Parts of a Circle
Arc (part of the circumference)

26. Parts of a Circle
Tangent (a line that touches the circle at a single point on the circumference

27. Parts of a Circle
Semicircle (half a circle)

28. What is this?
Radius

29. What is this?
Semicircle

30. What is this?
Centre

31. What is this?
Diameter

32. What is this?
Chord

33. What is this?
Sector

34. What is this?
Circumference

35. What is this?
Segment

36. What is this?
Tangent

37. What is this?
Diameter

38. What is this?
Sector

39. What is this?
Semicircle

40. What is this?
Segment

41. What is this?
Chord

42. What is this?
Tangent

43. What is this?
Arc

44. Learn these words (meanings & spellings)

45. Radius, Diameter and Circumference

46. Lines

47. Slices

48. Circumference
circumference
Circumference =
π × diameter
diameter

49. Example 1 Circumference = π × diameter Circumference = π × 4
Find the circumference of this circle
circumference
Circumference
= π × diameter
4cm
Circumference
= π × 4
= 12·57cm (2 d.p.)

50. Example 2 Circumference = π × diameter Circumference = π × 16
Find the circumference of this circle
circumference
Circumference
= π × diameter
8cm
Circumference
= π × 16
= 50·27cm (2 d.p.)

51. Area
Area
= π × radius × radius
= π × radius2
radius
area

52. Example 1 Area = π × radius × radius Area = π × 7 × 7
Find the area of this circle
Area
= π × radius × radius
7cm
Area
= π × 7 × 7
= 153·94cm² (2 d.p.)
area

53. Example 2 Area = π × radius × radius Area = π × 5 × 5
Find the area of this circle
Area
= π × radius × radius
10cm
Area
= π × 5 × 5
= 78·54cm² (2 d.p.)
area

54. Find the circumference and area of this circle
Question 1
Find the circumference and area of this circle
Circumference = π × diameter
Circumference = π × 9
= 28·27cm (2 d.p.)
9cm
Area = π × radius × radius
Area = π × 4·5 × 4·5
= 63·62cm² (2 d.p.)

55. Find the circumference and area of this circle
Question 2
Find the circumference and area of this circle
Circumference = π × diameter
Circumference = π × 12
= 37·70cm (2 d.p.)
6 cm
Area = π × radius × radius
Area = π × 6 x 6
= 113·10cm² (2 d.p.)

56. What is a prism?
A prism is a 3D shape that has the same cross-section all the way through. For example:
Triangular Prism
Hexagonal Prism
Cylinder

57. Calculating the volume of a prism:
Find the area of the cross-section then multiply by the length. Volume = Area of cross-section × length

58. Find the volume of this cylinder: Volume = 𝜋× 3 2 ×8 Volume = 226.2cm³
Two examples
Example 1
Example 2
Find the volume of this cylinder: Volume = 𝜋× 3 2 ×8 Volume = 226.2cm³
If the volume of this prism is 360cm³ and it is 9cm long, what is the area of the cross-section? Area of cross-section = 360 ÷ 9 Area of cross-section = 40cm²
3cm
8cm

59. Find the volume of this triangular prism:
Have a go:
Question 1
Find the volume of this triangular prism:
9cm
12cm
8cm
Answer: 432cm³

60. Volume of a cylinder
Area of circle (Πr2) x height

61. Volume of a Cylinder Diameter 40cm Height 25cm π x 20 x 20 x 25 =

62. Volume of a Cylinder π x 8 x 8 x 35 = 7037.17cm3 Radius = 8cm
Length = 35cm

63. Surface area

64. Surface Area
Surface area is the total area of the outside of a 3D object
Area A = 5 x 9
= 45cm2
Area B = 9 x 3
= 27cm2
Area C = 3 x 5
= 15cm2
Total Surface Area = ( ) x 2
= 174cm2 B C A
5cm
3cm
9cm

65. A Surface Area Each face is the same – a square. Area A = 5 x 5
= 25cm2
Total Surface Area = 6 x 25
= 150cm2
5cm A
5cm
5cm

66. C B A Surface Area Area A = 8 x 11 = 88cm2 Area B = 5 x 11 = 55cm2
Area C = 5 x 8
= 40cm2
TOTAL SURFACE AREA
= ( ) x 2
= 183 x 2
= 366cm2 C B
11cm A
5cm
8cm

67. Surface Area SA = 294cm2 SA = 378cm2 SA = 270cm2
Calculate the Surface Area of the cube and cuboids shown below:
SA = 294cm2
SA = 378cm2
15cm
7cm
3cm
EXTENSION:
8cm
SA = 270cm2
9cm
6cm
12cm
5cm

68. Your turn! Calculate the surface area of the following shapes. 5cm 9cm

69. Your turn! SA = 120cm2 SA = 216cm2 SA = 88m2
Calculate the surface area of the following shapes.
5cm
9cm
SA = 120cm2
14m
3cm
6cm
SA = 216cm2
4cm 1m 2m
SA = 88m2

70. Surface Area of a Cylinder
Can you see a cylinder is actually a rectangle with two small circles?
Surface Area of a Cylinder =
Area of rectangle +
(Area of circle x 2)

71. Surface Area of a Cylinder?
Circumference = π x 16 = 50.27cm
50.27 x 35 = cm2
Area of circle = π x 8 x 8 = cm2
x 2 =
= cm2
Radius = 8cm
Length = 35cm

72. Complete the Volume & Surface area worksheet

73. Answers
48cm3
88cm2

74. Answers
75.4cm3
100.53cm2

75. Answers
300cm3
360cm2

76. TOPIC TEST
You have 20 minutes to individually complete the AQA Topic Test

84. Directed Study

85. Metric and imperial units cross-number