1. Perimeter, area and volume – of everything!
GCSE Maths Lesson 10
Perimeter, area and volume – of everything!

2. Homework - metric and imperial measures sheet

8. Perimeter, area and volume

9. Review LOs
Know circle vocabulary and the formula for finding the circumference and the area of a circle
Find perimeters, areas and volumes of a variety of 2D and 3D shapes, including triangles, parallelograms, trapeziums, prisms, cones and pyramids, spheres

10. What do you know already?
Can you position the cards in the correct places to show how you would work out the perimeter, area or volume of each shape?

12. By the end of this lesson you will …
Know circle vocabulary and the formula for finding the circumference and the area of a circle
Find perimeters, areas and volumes of a variety of 2D and 3D shapes, including triangles, parallelograms, trapeziums, prisms, cones and pyramids, spheres

13. Perimeters, areas and volumes
Give out formulae card Units 1cm 1cm2 1cm3

14. Perimeter? Area?
4.5m

15. Perimeter? Area?
7.5m 4.5m

16. Area?
8cm 12cm

17. Area?

18. Perimeter? Area?

19. Area?

20. Perimeter
6.3cm 2.1cm 1.2cm 0.8cm Perimeter = = 20.8

21. Area
6.3cm 2.1cm 1.2cm 0.8cm Area = (6.3 x ( )) + (1.2 x 0.8) =(6.3 x 2.9) + (1.2 x 0.8) = = cm2

22. Can you …
… find the dimensions of a rectangle that has an area of 60 and a perimeter of 34? … find the length and width of a rectangle if its perimeter is 28cm and area is 48cm2? … find the dimensions of a rectangle whose perimeter is 54cm and area is 170cm2?

23. Surface Area and Volume
Cubes, cuboids and other prisms

24. Prisms A prism is a 3D shape that has a constant cross-section. CUBOID
TRIANGULAR
PRISM
CUBE

25. 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

26. 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

27. 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

29. Surface Area
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

30. Practice Calculate the surface area of the following shapes. 5cm 9cm

31. Volume of Prisms
Volume = area of cross-section x depth

32. Volume of Cuboids
A cuboid is a 3-dimensional object made up of a rectangles and squares
Volume = height x width x depth
Units: cm3, m3, mm3, km3, etc
height
depth
width

33. Volume of Prisms Volume = width x height x depth V = 4 x 3 x 12
V = 144cm3
12cm
3cm
4cm

34. Volume of Prisms Volume = Area of cross section x depth V = 7 x 9 x 3
V = 189cm3
7cm
3cm
9cm

35. Volume of Prisms Volume = Area of cross-section x depth
11cm
Area of cross section = (11 x 8) ÷ 2
= 44cm2
9cm
8cm
20cm
Volume = 44 x 20
= 880cm3
11cm 2 1 3
7mm
7mm
105m3
343mm3
5cm
80cm3 6m 5m
2cm 7m
8cm
7mm 6m

36. Worded Problems
A length of copper piping is in the shape of a triangular prism. The triangle on it’s end is a right angle, 9mm by 4mm by 10mm. The piece of pipe is 18cm long. What is the surface area of the pipe?
Area of Triangles = (9 x 4) ÷ 2
= 18mm2
= 18 x 2
= 36mm2
10mm
Front Rectangle = 180 x 10
= 1800mm2
9mm
180mm
Back Rectangle = 180 x 9
= 1620mm2
4mm
Total Surface Area =
= 4176mm2
Base Rectangle = 180 x 4
= 720mm2

37. Take care with metric conversions=
10mm
1cm
VOLUME = 1000mm3
VOLUME = 1cm3
10mm
1cm
10mm
1cm
x 1000
cm3
mm3
÷ 1000

38. Take care with metric conversions=
100cm 1m
VOLUME = cm3
VOLUME = 1m3
100cm 1m
100cm 1m x m3
cm3 ÷

39. Measurement Jeopardy.ppt

40. Review LOs
Know circle vocabulary and the formula for finding the circumference and the area of a circle
Find perimeters, areas and volumes of a variety of 2D and 3D shapes, including triangles, parallelograms, trapeziums, prisms, cones and pyramids, spheres

41. How many can you name?
How many can you name?

42. Circumference
circumference
Circumference =
π × diameter
diameter

43. 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.)

44. 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.)

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

46. 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

47. 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

48. 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.)

49. 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.)

50. Surface Area and Volume
Cylinders, Cones, Pyramids and Spheres

51. Real Life Cylinders

52. Cylinder
Volume = r2h
What is the volume of this cylinder?

53. Cones

54. Cones Pringles A third of the calories
If Pringles came in a cone, which was the same height and diameter as the tall tube, it would contain one third of the calories!!!
Why??
Pringles
A third
of the
calories

55. Cones
Volume =
Slant height (l)
Example: find the volume of this cone

56. Pyramids

57. Pyramids
Creamed
Coconut
1/3 of the
calories

58. Pyramids Volume = 1/3 x base area x height
Find the volume of this pyramid

59. Spheres 4/3π of the yumminess of a cube-shaped container!!
Find the volume of a sphere whose diameter is 15 cm
Volume =

60. The world's population is presently around 7 billion.
The average diameter of the Earth is m.
How much space is this per person?
Extension – Only 29% of the earth is land, how much land is there per person?

61. Surface Area of a Cone, Sphere & Cylinder Area & Volume Sphere Cone l
SA = π rl
SA =4 π r2
cylinder r h
SA = Curved surface area + Top + Bottom h
2 π r
Curved area =
= 2 π rh
SA = 2 π rh + 2 π r2

62. http://www. mathsbox. org
and

63. Surface Area of a Cone, Sphere & Cylinder
Calculate the Surface Area of a) d) 5 5 3 e) b) l
14.8 6 4 6 c)
5.2
r = 1.8

64. Complete this table Solid Volume Surface Area D = 10cm L = 15 cm
H = 13 cm
R = 3.5 cm
L = 9 cm
H = 60 m
L = 50 m
W = 40 m
D = 23 mm

65. Mini-Whiteboard Questions
Draw a rectangle with:
1. An area of 50cm2
2. An area of 50cm2 and a perimeter of 45cm
3. A perimeter of 40cm
4. A perimeter of 40cm and an area of 75cm2

66. Example exam questions
Topic test – further circumference and area

67. Review LOs
Know circle vocabulary and the formula for finding the circumference and the area of a circle
Find perimeters, areas and volumes of a variety of 2D and 3D shapes, including triangles, parallelograms, trapeziums, prisms, cones and pyramids, spheres

68. Review LOs
Know circle vocabulary and the formula for finding the circumference and the area of a circle
Find perimeters, areas and volumes of a variety of 2D and 3D shapes, including triangles, parallelograms, trapeziums, prisms, cones and pyramids, spheres

69. Homework

70. Perimeter, area and volume - Homework

71. What is the value of x? 6

72. The area of this shape is 20cm2.
What is the length, b ?
4cm
b cm 5

73. What is the perimeter of this shape?
2.5cm
2.5cm
2 cm 7

74. What is the volume of this shape?4

75. 2 The perimeter of this shape is 7cm. What is the missing length x?
x cm

76. What is the area of this shape?12

77. What is the surface area of this shape?18

78. The area of this shape is 46cm2.
What is the value of y? 23

79. The area of this square is 100cm2.
What is the length of each side? 10

80. 1 The perimeter of this rectangle is 18cm What is the value of y? y cm

81. 3

82. The area of this shape is 130cm2.
What is the length, b ? 13
10cm
b cm

83. 11 The perimeter of this rectangle is 28cm What is the value of y? 3cm

84. 8

85. 6cm
4cm
6cm 9

86. What is the perimeter of this shape?14

87. 15

88. What is the area of this shape?19
9.5cm

89. What is the perimeter of this shape?16

90. What is the area of this shape?17
8.5cm

91. 3cm
What is the area of this shape?
4cm 20
Clue

92. 21 The perimeter of this shape is 71cm. What is the missing length x?
x cm

93. What is the perimeter of this shape?22
7cm
4cm

94. The area of this shape is 20cm2.
What is the perimeter? 24

95. Also for homework
SYWAGC – circles

96. Also for homework?
Topic test circles

97. Two-way tables and frequency trees.

98. How could we display the information below in an easier format
How could we display the information below in an easier format? A school chess club has 70 members of which 40 are boys. Students play in competitions on a regular basis. Last month, 13 girls and 11 boys played in competitions.
2 of 4
AQA Education (AQA) is a registered charity (number ) and a company limited by guarantee registered in England and Wales (number ). Our registered address is AQA, Devas Street, Manchester M15 6EX.

99. A two way table might be helpful….
Played in competition last month
Did not play in competition last month
Boys 11 29 40
Girls 13 17 30 24 46 70
What other methods might we use to display the information?
3 of 4
AQA Education (AQA) is a registered charity (number ) and a company limited by guarantee registered in England and Wales (number ). Our registered address is AQA, Devas Street, Manchester M15 6EX.

100. 11 40 Boys 29 70 13 Girls 30 17 Use a frequency tree
Played in competition 11 40
Boys
Didn’t play in competition 29 70
Played in competition 13
Girls 30 17
Didn’t play in competition
4 of 4
Copyright © 2015 AQA and its licensors. All rights reserved.
AQA Education (AQA) is a registered charity (number ) and a company limited by guarantee registered in England and Wales (number ). Our registered address is AQA, Devas Street, Manchester M15 6EX.

101. x of x Version 3.0
Copyright © AQA and its licensors. All rights reserved.

102. x of x Version 3.0
Copyright © AQA and its licensors. All rights reserved.

103. In Year 6 at a local primary school there are 120 students
In Year 6 at a local primary school there are 120 students. The ratio of boys to girls is 9:6. The girls were twice as likely to own a mobile phone as they were to not own a mobile phone. The ratio of boys who own a mobile phone to those who don’t own a mobile phone is 5:3
2 of 3
AQA Education (AQA) is a registered charity (number ) and a company limited by guarantee registered in England and Wales (number ). Our registered address is AQA, Devas Street, Manchester M15 6EX.

104. 45 72 Boys 27 120 32 Girls 48 16 Use a frequency tree
Owns a mobile phone 45 72
Boys
Doesn’t own a mobile phone 27
120
Owns a mobile phone 32
Girls 48
Doesn’t own a mobile phone 16
3 of 3
Copyright © 2015 AQA and its licensors. All rights reserved.
AQA Education (AQA) is a registered charity (number ) and a company limited by guarantee registered in England and Wales (number ). Our registered address is AQA, Devas Street, Manchester M15 6EX.

105. What did we do last time? 1.

106. 2.

107. 3.

108. 4.

109. 5.

110. 6.

111. 7.

112. 8.

113. Last bit of probability for now - tree diagrams

114. TREE DIAGRAMS
First coin
Second coin H H T H T T

115. H T

116. H T

117. Imagine choosing a ball from this bag and then replacing it
Imagine choosing a ball from this bag and then replacing it. If you did this three times, what's the probability that you would pick at least one green ball? What’s the best method to use to answer this question? What if you didn't replace the ball each time?

118. Replacing it - if you did this three times, what's the probability that you would pick at least one green ball?

119. Not replacing it - if you did this three times, what's the probability that you would pick at least one green ball?

120. Two cards are drawn from a pack with replacement13 52 39
A spade
Not a spade
1st card
2nd card

121. Two cards are drawn from a pack without replacement13 52 39
A spade
Not a spade
1st card
2nd card

122. Exam question 11

123. Looking back at targets
Do you understand that the sum of the probabilities of all possible mutually exclusive outcomes is 1?
Do you understand the difference between theoretical and experimental probability?
Can you calculate probability using a tree diagram?

124. Probability revision quiz HIGHER
In teams of 3
work together
to answer all
the questions

125. Finding probabilities 1 (words)
5 points
10 points
15 points
P(roll an odd number on a dice) is
P(it will rain tomorrow) is
P(baby born is a girl) is
P(being younger tomorrow) is
P(win lottery) is
P(sun rising tomorrow) is

126. Finding probabilities 2 (fractions)
5 points
(dice)
10 points
(cards)
15 points
P(red prime)=
P(black)=
P(4)=
P(even)=
P(red picture card)=
P(less than 5) =

127. Finding probabilities 3 (OR rule)
5 points
(dice)
10 points
(cards)
15 points
P(prime or square)=
P(6 or 7)=
P(4 or 5)=
P(2, 3 or 4)=
P(red 3 or black queen)=
P(2 or 3) =

128. Finding probabilities 4 (2 events)
5 points
(2 dice)
10 points
15 points
P(2 numbers the same)=
P(5 or 6)=
P( 7 )=
P(13)=
P(less than 4) =
P(even) =
You have 1 minute
to list all the outcomes
of 2 dice before the
questions come up.

129. Finding probabilities 5 (biased dice)1 2 3 4 5 6
0.2
0.1
0.05 x
0.15
5 points
10 points
15 point
P(not 4)=
P(6)=
P(2)=
P(1 or 3)=
P(not 2)=
P(odd) =

130. Finding probabilities 6 (tree diagrams)
Copy down this information:
The probability it rains on a Monday is 0.3
The probability it rains on Tuesday is 0.25
5 points
20 points
30 points
P( it rains on both days)
Draw a tree diagrams to show all outcomes
P( it does not rain on Monday)=
P(It does not rain on Tuesday)=

131. Bonus question (40 points)
Based on the following tree diagram what is the probability I pick 2 different colours?

132. Relative frequency in a graph

133. PLENARY
Who wants to be a millionaire? millionaire_probability.ppt

134. Need to do recurring decimals

135. Still to do
Use pi in an answer