measurement, area, surface area and volume · 94 excel essential skills: year 9 mathematics...

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Mathletics Instant

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Mathletics Instant

Workbooks

Measurement, Area, Surface Area and Volume

Teacher Book - Series J-2

94 EXCEL ESSENTIAL SKILLS: YEAR 9 MATHEMATICS REVISION AND EXAM WORKBOOK 2 – EXTENSION

Measurement, area, surfacearea and volume

TOPIC TEST SECTION 1

1 Find the area of a square with side length 12 cm.

A 48 cm2 B 288 cm2 C 144 cm2 D None of these

2 Calculate the volume of a cube with side length 5 cm.


3 A rectangular prism has sides of length 9 cm, 11 cm and 12 cm. Find its volume.

A 32 cm3 B 339 cm3 C 594 cm3 D 1188 cm3

4 A cube has a volume of 4913 cm3. Find the length of each side of the cube.

A 70 cm B 8.4 cm C 181 cm D 17 cm

5 Find the perimeter of a square of side 4.2 cm.

A 17.64 cm B 74.1 cm C 16.8 cm D None of these

6 If the perimeter of a square is 36 cm, then the area of the square is

A 6 cm2 B 9 cm2 C 36 cm2 D 81 cm2

7 How many square centimetres are there in a square metre?

A 100 B 1000 C 10 000 D 100 000

8 The radius of the Earth is approximately 6400 km. What is the circumference of theEarth at the equator?

A 40 212 km B 1.29 × 108 km C 20 106 km D 38 340 km

9 What is the area of a circle of radius 3.2 m? Answer to the nearest square metre.

A 101 m2 B 32 m2 C 129 m2 D 8 m2

10 The volume of a rectangular prism is 216 cm3. Find the total surface area of a cubehaving the same volume.

A 64 cm2 B 216 cm2 C 144 cm2 D 196 cm2

Marks

Total marks achieved for SECTION 110

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1

1

Measurement, area, surface area and volumeInstructions for SECTION 1 • You have 15 minutes to answer Section 1

• Each question is worth 1 mark• Attempt ALL questions• Calculators may be used• Fill in only ONE CIRCLE for each question









A 32 cm3 B 339 cm3 C 594 cm3 D 1188 cm3


A 70 cm B 8.4 cm C 181 cm D 17 cm




A 6 cm2 B 9 cm2 C 36 cm2 D 81 cm2


A 100 B 1000 C 10 000 D 100 000


A 40 212 km B 1.29 × 108 km C 20 106 km D 38 340 km


A 101 m2 B 32 m2 C 129 m2 D 8 m2


A 64 cm2 B 216 cm2 C 144 cm2 D 196 cm2

Marks


1

1

1

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iiMeasurement, area, surface area and volumeMathletics Instant Workbooks – Series J 2 Copyright © 3P Learning

Measurement, area, surface area and volumeTopic Test PART A

Marks

Total marks achieved for PART A 10

Instructions This part consists of 10 multiple-choice questions Each question is worth 1 mark Attempt ALL questions Calculators are NOT to be used Fill in only ONE CIRCLE for each question

Time allowed: 15 minutes Total marks = 10

Total marks achieved for PART B 15

Marks

Measurement, area, surface area and volumeTopic Test PART B

iiiMeasurement, area, surface area and volumeMathletics Instant Workbooks – Series J 2 Copyright © 3P Learning

Instructions This part consists of 15 questions Each question is worth 1 mark Attempt ALL questions Calculators may be usedTime allowed: 20 minutes Total marks = 15

Questions Answers only

95Chapter 10: Measurement, area, surface area and volume



Marks


1 State the formula for the area of a circle. ___________________

2 Convert 1.68 m2 to cm2. ___________________

3 What is the side length of a square that has an area of 160 000 m2? ___________________

4 How many square metres in 2 hectares? ___________________

5 Calculate the surface area of a cube of side 2.5 m. ___________________

6 Calculate the volume of a rectangular prism 3.5 m long,3.4 m wide and 2.8 m high. ___________________

7 Calculate the circumference of a circle with radius equal to 5 cm. ___________________

For the solid given, calculate:

8 the area of rectangle BCDH. ___________________

9 the area of triangle ABH. ___________________

10 the area of AHFG. ___________________

11 the total surface area. ___________________

12 the volume. ___________________

13 A cube has a volume of 3375 cm3. Find the length of each sideof the cube. ___________________

14 Find the perimeter of a square of side 5.6 cm. ___________________

15 The volume of a cube is 512 cm3. Find its surface area. ___________________

Questions Answers

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Measurement, area, surface area and volume

Instructions for SECTION 2 • You have 20 minutes to answer ALL of Section 2• Each question is worth 2 marks• Attempt ALL questions• Calculators may be used

10 m8 m

5 m

4 m

B

AG

HF

C D

E

95Chapter 10: Measurement, area, surface area and volume



Marks


1 State the formula for the area of a circle. ___________________

2 Convert 1.68 m2 to cm2. ___________________

3 What is the side length of a square that has an area of 160 000 m2? ___________________

4 How many square metres in 2 hectares? ___________________

5 Calculate the surface area of a cube of side 2.5 m. ___________________

6 Calculate the volume of a rectangular prism 3.5 m long,3.4 m wide and 2.8 m high. ___________________

7 Calculate the circumference of a circle with radius equal to 5 cm. ___________________

For the solid given, calculate:

8 the area of rectangle BCDH. ___________________

9 the area of triangle ABH. ___________________

10 the area of AHFG. ___________________

11 the total surface area. ___________________

12 the volume. ___________________

13 A cube has a volume of 3375 cm3. Find the length of each sideof the cube. ___________________

14 Find the perimeter of a square of side 5.6 cm. ___________________

15 The volume of a cube is 512 cm3. Find its surface area. ___________________

Questions Answers

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Measurement, area, surface area and volume

Instructions for SECTION 2 • You have 20 minutes to answer ALL of Section 2• Each question is worth 2 marks• Attempt ALL questions• Calculators may be used

10 m8 m

5 m

4 m

B

AG

HF

C D

E









A 32 cm3 B 339 cm3 C 594 cm3 D 1188 cm3


A 70 cm B 8.4 cm C 181 cm D 17 cm




A 6 cm2 B 9 cm2 C 36 cm2 D 81 cm2


A 100 B 1000 C 10 000 D 100 000


A 40 212 km B 1.29 × 108 km C 20 106 km D 38 340 km


A 101 m2 B 32 m2 C 129 m2 D 8 m2


A 64 cm2 B 216 cm2 C 144 cm2 D 196 cm2

Marks


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A 32 cm3 B 339 cm3 C 594 cm3 D 1188 cm3


A 70 cm B 8.4 cm C 181 cm D 17 cm




A 6 cm2 B 9 cm2 C 36 cm2 D 81 cm2


A 100 B 1000 C 10 000 D 100 000


A 40 212 km B 1.29 × 108 km C 20 106 km D 38 340 km


A 101 m2 B 32 m2 C 129 m2 D 8 m2


A 64 cm2 B 216 cm2 C 144 cm2 D 196 cm2

Marks


1

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A 32 cm3 B 339 cm3 C 594 cm3 D 1188 cm3


A 70 cm B 8.4 cm C 181 cm D 17 cm




A 6 cm2 B 9 cm2 C 36 cm2 D 81 cm2


A 100 B 1000 C 10 000 D 100 000


A 40 212 km B 1.29 × 108 km C 20 106 km D 38 340 km


A 101 m2 B 32 m2 C 129 m2 D 8 m2


A 64 cm2 B 216 cm2 C 144 cm2 D 196 cm2

Marks


1

1

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A 32 cm3 B 339 cm3 C 594 cm3 D 1188 cm3


A 70 cm B 8.4 cm C 181 cm D 17 cm




A 6 cm2 B 9 cm2 C 36 cm2 D 81 cm2


A 100 B 1000 C 10 000 D 100 000


A 40 212 km B 1.29 × 108 km C 20 106 km D 38 340 km


A 101 m2 B 32 m2 C 129 m2 D 8 m2


A 64 cm2 B 216 cm2 C 144 cm2 D 196 cm2

Marks


1

1

1

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A 32 cm3 B 339 cm3 C 594 cm3 D 1188 cm3


A 70 cm B 8.4 cm C 181 cm D 17 cm




A 6 cm2 B 9 cm2 C 36 cm2 D 81 cm2


A 100 B 1000 C 10 000 D 100 000


A 40 212 km B 1.29 × 108 km C 20 106 km D 38 340 km


A 101 m2 B 32 m2 C 129 m2 D 8 m2


A 64 cm2 B 216 cm2 C 144 cm2 D 196 cm2

Marks


1

1

1

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A 32 cm3 B 339 cm3 C 594 cm3 D 1188 cm3


A 70 cm B 8.4 cm C 181 cm D 17 cm




A 6 cm2 B 9 cm2 C 36 cm2 D 81 cm2


A 100 B 1000 C 10 000 D 100 000


A 40 212 km B 1.29 × 108 km C 20 106 km D 38 340 km


A 101 m2 B 32 m2 C 129 m2 D 8 m2


A 64 cm2 B 216 cm2 C 144 cm2 D 196 cm2

Marks


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A 32 cm3 B 339 cm3 C 594 cm3 D 1188 cm3


A 70 cm B 8.4 cm C 181 cm D 17 cm




A 6 cm2 B 9 cm2 C 36 cm2 D 81 cm2


A 100 B 1000 C 10 000 D 100 000


A 40 212 km B 1.29 × 108 km C 20 106 km D 38 340 km


A 101 m2 B 32 m2 C 129 m2 D 8 m2


A 64 cm2 B 216 cm2 C 144 cm2 D 196 cm2

Marks


1

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A 32 cm3 B 339 cm3 C 594 cm3 D 1188 cm3


A 70 cm B 8.4 cm C 181 cm D 17 cm




A 6 cm2 B 9 cm2 C 36 cm2 D 81 cm2


A 100 B 1000 C 10 000 D 100 000


A 40 212 km B 1.29 × 108 km C 20 106 km D 38 340 km


A 101 m2 B 32 m2 C 129 m2 D 8 m2


A 64 cm2 B 216 cm2 C 144 cm2 D 196 cm2

Marks


1

1

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A 32 cm3 B 339 cm3 C 594 cm3 D 1188 cm3


A 70 cm B 8.4 cm C 181 cm D 17 cm




A 6 cm2 B 9 cm2 C 36 cm2 D 81 cm2


A 100 B 1000 C 10 000 D 100 000


A 40 212 km B 1.29 × 108 km C 20 106 km D 38 340 km


A 101 m2 B 32 m2 C 129 m2 D 8 m2


A 64 cm2 B 216 cm2 C 144 cm2 D 196 cm2

Marks


1

1

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A 32 cm3 B 339 cm3 C 594 cm3 D 1188 cm3


A 70 cm B 8.4 cm C 181 cm D 17 cm




A 6 cm2 B 9 cm2 C 36 cm2 D 81 cm2


A 100 B 1000 C 10 000 D 100 000


A 40 212 km B 1.29 × 108 km C 20 106 km D 38 340 km


A 101 m2 B 32 m2 C 129 m2 D 8 m2


A 64 cm2 B 216 cm2 C 144 cm2 D 196 cm2

Marks


1

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A 32 cm3 B 339 cm3 C 594 cm3 D 1188 cm3


A 70 cm B 8.4 cm C 181 cm D 17 cm




A 6 cm2 B 9 cm2 C 36 cm2 D 81 cm2


A 100 B 1000 C 10 000 D 100 000


A 40 212 km B 1.29 × 108 km C 20 106 km D 38 340 km


A 101 m2 B 32 m2 C 129 m2 D 8 m2


A 64 cm2 B 216 cm2 C 144 cm2 D 196 cm2

Marks


1

1

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A 32 cm3 B 339 cm3 C 594 cm3 D 1188 cm3


A 70 cm B 8.4 cm C 181 cm D 17 cm




A 6 cm2 B 9 cm2 C 36 cm2 D 81 cm2


A 100 B 1000 C 10 000 D 100 000


A 40 212 km B 1.29 × 108 km C 20 106 km D 38 340 km


A 101 m2 B 32 m2 C 129 m2 D 8 m2


A 64 cm2 B 216 cm2 C 144 cm2 D 196 cm2

Marks


1

1

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A 32 cm3 B 339 cm3 C 594 cm3 D 1188 cm3


A 70 cm B 8.4 cm C 181 cm D 17 cm




A 6 cm2 B 9 cm2 C 36 cm2 D 81 cm2


A 100 B 1000 C 10 000 D 100 000


A 40 212 km B 1.29 × 108 km C 20 106 km D 38 340 km


A 101 m2 B 32 m2 C 129 m2 D 8 m2


A 64 cm2 B 216 cm2 C 144 cm2 D 196 cm2

Marks


1

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A 32 cm3 B 339 cm3 C 594 cm3 D 1188 cm3


A 70 cm B 8.4 cm C 181 cm D 17 cm




A 6 cm2 B 9 cm2 C 36 cm2 D 81 cm2


A 100 B 1000 C 10 000 D 100 000


A 40 212 km B 1.29 × 108 km C 20 106 km D 38 340 km


A 101 m2 B 32 m2 C 129 m2 D 8 m2


A 64 cm2 B 216 cm2 C 144 cm2 D 196 cm2

Marks


1

1

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A 32 cm3 B 339 cm3 C 594 cm3 D 1188 cm3


A 70 cm B 8.4 cm C 181 cm D 17 cm




A 6 cm2 B 9 cm2 C 36 cm2 D 81 cm2


A 100 B 1000 C 10 000 D 100 000


A 40 212 km B 1.29 × 108 km C 20 106 km D 38 340 km


A 101 m2 B 32 m2 C 129 m2 D 8 m2


A 64 cm2 B 216 cm2 C 144 cm2 D 196 cm2

Marks


1

1

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Answers – Measurement, area, surface area and volume

Mathletics Instant Workbooks – Series J 2 Copyright © 3P Learning

123Answers

Answers

PAGE 88 1 a acute angled triangle b right angled triangle c obtuse angled triangle d scalene triangle e equilateral triangle f isosceles triangle2 a square b rectangle c parallelogram d rhombus e trapezium f kite 3 a pentagon b hexagon c heptagon d octagon e nonagonf decagon 4 a circle b ellipse c sector

PAGE 89 1 a 3, 1, 180° b 4, 2, 360° c 5, 3, 540° d 6, 4, 720° e 7, 5, 900° f 8, 6, 1080° g 9, 7, 1260° h 10, 8, 1440° i 11, 9, 1620°j 12, 10, 1800° 2 a 180° b 360° c 540° d 720° e 900° f 1080° g 1260° h 1440° i 1620° j 1800° k (n – 2)180° l 360°

PAGE 90 1 a A bh= 12

b A s= 2 c A lb= d A bh= e A xy= 12

f A h a b= +( )12

g A xy= 12

h A r= π 2 i A r=°

×θ π360

2

2 a 15.68 cm2 b 56.7 cm2 c 37.21 cm2 d 70 cm2 e 105.84 cm2 f 41.6 cm2 g 18 cm2 h 60 cm2 i 153.9 cm2 j 73.1 cm2 k 189 cm2 l 96 cm2

PAGE 91 1 a 318 cm2 b 121.5 cm2 c 380.22 cm2 2 a 736 cm2 b 712.8 cm2 c 187.2 cm2 3 a 337.2 m2 b 279.4 m2 c 637.95 m2

4 a 502.65 cm2 b 452.4 cm2 c 1218.3 cm2

PAGE 92 1 a 195.1 cm3 b 188.2 cm3 c 213.6 cm3 2 a 1220 cm3 b 223.2 cm3 c 1235 cm3 3 a 6117.53 cm3 b 351.00 m3

c 1716.63 cm3 4 a 1072.5 m3 b 1968 m3 c 520 m3

PAGE 93 1 a 1131.0 cm3 b 3016.0 cm3 c 1924.2 cm3 2 a 905 cm3 b 6160 cm3 c 435 cm3 3 a 295.56 cm3 b 3848.45 cm3

c 664.16 cm3 4 a 7754.7 cm3 b 1012.1 cm3 c 695.2 cm3

PAGE 94 1 C 2 B 3 D 4 D 5 C 6 D 7 C 8 A 9 B 10 B

PAGE 95 1 A r= π 2 2 16 800 cm2 3 400 m 4 20 000 m2 5 37.5 m2 6 33.32 m3 7 31.4 cm 8 40 m2 9 25 m2 10 56.57 m2

11 387.14 m2 12 520 m3 13 15 cm 14 22.4 cm 15 384 cm2

PAGE 96 1 B 2 C 3 C 4 A 5 C 6 A 7 C 8 C 9 D 10 C

PAGE 97 11 0.102 12 0.375 13 40% 14 34 15 9 16 140 seconds 17 4 06 10 4. × − 18 9a + 3ab 19 3ab (2a – 1) 20 x = 5.5 21 x = 6

22 x < 2 15

23 $90 24 8 m 25 5 7 3−

PAGE 98 26 289° 27 35° 28 $70 29 10 6− 30 712

a 31 11.5 32 x

y= − 82

33 −23

34 1

2n 35 3 2mn

PAGE 99 36 a y = 2 b –a + 12 c 15.6 m2 d a116 e a = −17 1

2 37 a x = 1, y = –5

PAGE 100 37 b P xy

= 49 2 c x ≤ 6 0 6 d T = 40.3 e 2x – y + 1 = 0 38 a $71.63 b $1830 c $31 666.67

PAGE 101 1 C 2 B 3 D 4 C 5 C 6 A 7 D 8 A 9 D 10 A

PAGE 102 11 1 12 2 34

tonnes 13 10 : 11 14 9

16 15 0.1 16 15 and 9 17 107 18 6 19 x = 5 20 2 16 104. × 21 216 22 13 23 2 6

3b a

ab−

PAGE 103 24 3

4 2x 25 P A

RT= 100 26 x = 0 27 8 28 x = 2 29 6 6 30 10 3 31 2 22x xy− 32

x yxy+

33 2 2p q−( ) 34 3 22

35 0.0225

PAGE 104 36 a m a b c+ −( ) b 3 1 3 1x x+( ) −( ) c x x−( ) −( )2 3 d a b a b a b2 2+( ) +( ) −( ) e 1 1 2+( ) +( )p p 37 a 52

b − −5 2 6

PAGE 105 37 c xx

+−

75 d

3 13 1x

x x+

+( ) −( ) e −

+( ) −( )1

1 1x x x 38 a (0, 0) b AB BC= = 4 2 c m m1 2 1= − d (2, 2) e 1

PAGE 106 1 B 2 A 3 B 4 A 5 D 6 D 7 B 8 C 9 C 10 C

PAGE 107 11 $880 12 4 6a 13 a b2 2− 14 4 7 15 27 cm3 16 1

20 000 17 xy2 18 120 km/h 19 942.21 20 0.0025 L 21 0.0041818

22 x = 4 23 4 2xy 24 x = 9 25 x xy x y y3 2 2 3+ + +

PAGE 108 26 8m – 4 27 3 28 0.01 km2 29 ab units2 30 x = 8 cm 31 3 2x 32 26.686 33 Trapezium 34 3 h 12 min 35 25

PAGE 109 36 a y BA

= ± b a = 5 c p = 7 d m = 42 e x = 3, y = 3

PAGE 110 37 a x = 45° b x = 70° c x = 60° d x = 50° 38 a 43.88 m2 b 168.25 cm2

PAGE 111 1 D 2 B 3 C 4 B 5 D 6 C 7 A 8 B 9 B 10 D

PAGE 112 11 a 12 A h a b= +( )12

13 x

x+ 3

14 1 15 3 22x x+ − 16 87.5% 17 7 18 27 9a 19 ab a b−( ) 20 1

7 21 9 22 a32

23 − 23 24 12.5%

PAGE 113 25 12 6x 26 44° 27 $23 231.25 28 a b2 225− 29 x = 150° co-interior angles are supplementary 30 $759.50 31 8

5x

32 x = 16 33 27 9 9x y 34 7 1 1a a+( ) −( ) 35 7 6

15x +

1

2

3

4

5

6

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measurement, area, surface area and volume · 94 excel essential skills: year 9 mathematics...

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