Chapter11-Volume, Mass and Time

11

Measurement

Volume, mass and time

Measuring things is an important part of our lives: ‘How long till my birthday?’ ‘How heavy is my school bag?’ ‘How much water is needed to fill the swimming pool?’ If you worked in a kitchen, you would be measuring all the time: ‘How much flour is needed for a cake?’ ‘What amount of water is needed to cook spaghetti?’ ‘For how long do we roast a chicken?’ In this chapter, we look at how to measure volume, capacity, mass and time.

In this chapter you will: ■ ■ ■ ■ ■ ■ ■ ■ ■ ■

estimate, measure and convert volumes (cubic millimetres, cubic centimetres and cubic metres) find the volume of a rectangular prism estimate, measure and convert capacities (millilitres, litres and kilolitres) know and use the relationships 1 cm 3 = 1 mL, and 1 m 3 = 1 kL estimate, measure and convert masses (milligrams, grams, kilograms and tonnes) draw and interpret timelines using a scale round times to the nearest minute or hour add and subtract times and calculate time differences use time zones to calculate time differences between major cities interpret and use timetables.

Wordbank ■ ■ ■ ■ ■ ■

volume The amount of space occupied by an object. cubic metre The volume of a cube with side length 1 metre. capacity The amount of fluid (liquid or gas) contained by an object. tonne A measuring unit of mass for heavy objects. time zone A region of the world in which all places experience the same time of day. Eastern Standard Time The time zone for the eastern states of Australia.

Think! Is there a difference between volume and mass? Do they mean the same thing? ■ Can you explain what they are in your own words? ■ Are big things always heavy? ■ Can a big thing be light, or a small thing be heavy? ■ ■

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Start up Worksheet 11-01 Brainstarters 11

1 Each cube in these drawings represents one cubic centimetre (1 cm3). Find the volume of each figure. a b c d

Skillsheet 11-01 Units of time

Skillsheet 11-02 Telling the time

e

f

g

h

i

j

k

l

2 Write the time shown on each of these clocks. a 11

12

b 1

11

10

2

8

4

9

d 11

6 12

6 12

6

11

12

5

1

10

2

8

4

9

3 4 6

3

f 2

7

4

1

8

5

8 7

9

1 2

5

10

12

10 9

3

11

4

8

Skillsheet 11-03 24-hour time

4

e

3

6

8

1 2

7

2

7

9

11

10

5

10

c 1

9

3

7

12

5

3

7

6

5

3 Write the times shown on these watches using 12-hour time (am or pm). a

b

04:15

Worksheet 11-02 TV times

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c

13:20

20:17

4 Write these as 24-hour times: a 4:00pm b 1:00am d 5:15am e 6:38pm g 8:46am h 9:30pm

c 3:30am f 12:30pm i 10:17pm

5 Write these 24-hour times as 12-hour times: a 1800 hours b 0400 hours d 0530 hours e 1330 hours g 1930 hours h 2005 hours j 0630 hours k 1015 hours

c f i l

2200 hours 1915 hours 2145 hours 1140 hours

6 Test your general knowledge by answering these questions. b How many years in a century? a What is the meaning of BC and AD? c How many months in a year? d How many hours in a day? e How many minutes in an hour? f How many days in a year? g How many days in a month? h How many weeks in a year? i What is a leap year? Why are leap years necessary? 7 A leap year occurs when the year can be evenly divided by 4, except for years ending in 00 that are not exactly divisible by 400. The year 2000 was a leap year because it is divisible by 400. The year 2100 is not a leap year because it is not divisible by 400. a Make a list of all the leap years are there between 1891 and 1925. b How many leap years are there between 1991 and 2121? 8 Calculate: a 5 × 100 d 7000 ÷ 1000 g 6.01 ÷ 10

b 26 × 1000 e 350 × 100 h 4.05 ÷ 100

c 1800 ÷ 10 f 2.4 × 100 i 13.71 × 1000

Skillsheet 8-01 Multiplying by 10, 100, 1000

Volume The volume of a solid is the amount of space occupied by the solid.

Working mathematically Applying strategies: Comparing volumes 1 Bring to school as many different containers as you can find. As a group, arrange them in order, from smallest volume (occupying the least space) to largest volume (occupying the most space). 2 Write how the order was decided. 3 Check your estimates by filling the containers with either water or sand and comparing results. 4 Discuss your results with your teacher. VOLUME, MASS AND TIME

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How to measure volume Often informal (everyday) units are used to refer to volume. For example: cup • a cup of flour • a cup of milk

Exercise 11-01 1 Write an example of the items that could be measured by each of these units. a cup(s) b box(es) c handful d pinch e bucket(s) f packet g capsule(s) h can(s) i teaspoon j wheelbarrow k carton l capful

Standard units of volume As with all measurements, we need agreed units for measuring volume. These are based on the cube. 1 cubic millimetre A cubic centimetre is the amount of space that a cube with each side measuring 1 cm would occupy. The volume of the cube is one cubic centimetre, or 1 cm3. 1 cm A cubic millimetre is the amount of space that a cube with each side 1 cm measuring 1 mm would occupy. The volume of the red cube is one cubic 1 cm millimetre, or 1 mm3. There are 1000 cubic millimetres in one cubic 1 cubic centimetre centimetre. A cubic metre is the amount of space that a cube with each side 1 m would occupy, that is 1 m3. It is about the size of a box containing a large TV set. A shower recess is about 2.5 m3. There are 1 000 000 cubic centimetres in one cubic metre. The greatly reduced diagram below illustrates this. 100 cm (or 1 m)

100 cm (or 1 m)

100 cm (or 1 m)

356

1 m3 = 100 cm × 100 cm × 100 cm = 1 000 000 cm3 NEW CENTURY MATHS 7

1 cm3

1000 mm3

1 cm3 = 10 mm × 10 mm × 10 mm = 1000 mm3

1 cm 1 cm

10 mm 10 mm

1 cm

10 mm

Unit cubic millimetre cubic centimetre cubic metre

Abbreviation mm3 cm3 m3

Conversion 1 cm3 = 1000 mm3 1 m3 = 1 000 000 cm3

The diagram below will help you convert units. × 1 000 000

m3

× 1000

cm3

mm3

÷ 1 000 000

÷ 1000

Example 1 1 Convert 12 000 mm3 into cm3.

Solution mm3 → cm3 (÷1000)

12 000 mm3 = (12 000 ÷ 1000) cm3 = 12 cm3

2 Convert 48 m3 into cm3.

Solution m3 → cm3 (× 1 000 000)

48 m3 = (48 × 1 000 000) cm3 = 48 000 000 cm3

Exercise 11-02 1 Copy and complete: mm3 a 3 cm3 = mm3 c 2.6 cm3 = cm3 e 7.2 m3 = mm3 g 1 m3 = i 126 000 000 cm3 = mm3 k 25 m3 = m3 m 63 000 cm3 =

Example 1

m3

b d f h j l n

5 m3 = cm3 4000 mm3 = cm3 66 000 mm3 = cm3 2300 cm3 = m3 3450 mm3 = cm3 78 000 mm3 = m3 1.4 mm3 = cm3

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2 Use any types of cubes to complete these constructions. a Build as many different solids as you can with a volume of 3 cubes (that is using 3 cubes). Sketch each one. b Build as many different solids as you can with a volume of 4 cubes (that is using 4 cubes). Sketch each one. c Build as many different solids as you can with a volume of 5 cubes. Sketch each one. 3 Match the correct volume (A to G) with each of the items (a to g) listed. a a bottle of liquid paper A 200 m3 b a box of tissues B 3890 m3 c a glass of water C 1250 cm3 d a bottle of lemonade D 5000 cm3 e a class room E 20 000 mm3 f a school hall F 250 cm3 g a cereal package G 2200 cm3 CAS 11-01 Volume conversions

4 Use this link to discover how Computer Algebra Software can be used to help you convert units of volume.

Working mathematically Applying strategies: Build a cubic metre As a group activity, construct your own cubic metre. Write a short report on how you did it.

Worksheet 11-03 Volume

Volume of a rectangular prism Example 2 This rectangular prism is made from 1 cm cubes. What is its volume?

16 cubes in one layer

3 layers

Solution The cube has three layers. Each layer contains 16 cubes (count them). Volume of the cube = (16 × 3) cm3 = 48 cm3

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Exercise 11-03 1 The shapes below are made of 1 cm cubes. Copy and complete the following table. Shape

Number of cubes in one layer

Number of layers

Example 2

Volume (cm3)

a b c d e f a

b

c

d

e

f

Finding the rule In Exercise 11-03, the number of cubes in each layer equals the ‘length multiplied by the breadth (width)’ of the base of the prism (shaded darkest orange). This product is the area of the base. The number of layers is the height. This gives a rule for finding the volume of a rectangular prism: Volume of a rectangular prism = area of base × height = length × breadth × height V=l×b×h VOLUME, MASS AND TIME

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The volume of a rectangular prism is: V = length × breadth × height V=l×b×h

Example 3 Find the volume of the rectangular prism on the right.

8 cm

Solution

V = area of base × height =l×b×h = 18 × 12 × 8 = 1728 The volume is 1728 cm3.

base

12 cm

18 cm

Exercise 11-04 Example 3

1 Find the volume of each of these rectangular prisms. a b

4 cm

c

4 cm 9 cm

21 cm

5 cm

36 cm

3 cm

5 cm

17 cm

d

17 cm

e 3 cm

f 15 cm

3m

3 cm 3 cm

9 cm

11 m

15 cm 15 cm

g m

0c

18

1.2 m 2.4 m

h

1.8 m 33.5 m

Spreadsheet 11-01 Volume of rectangular prisms

2 The table on the next page gives the dimensions of different rectangular prisms. Copy and complete it. (This exercise can also be done using a spreadsheet. Use this link to produce and complete the table.)

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NEW CENTURY MATHS 7

Prism

Length

Width

Height

a

50 cm

50 cm

50 cm

b

5 cm

10 cm

18 cm

c

4m

2.5 m

1.4 m

d

24 mm

16 mm

11 mm

10 cm

10 cm

e f

5 mm

100 mm3

1.5 m 22 cm

i

70 mm

j

1.8 m

2000 cm3

2 mm

g h

Volume

3m

27 m3

5 cm

880 cm3 70 000 mm3

10 mm

9 m3

10 m

3 Find the volume of each of these shapes. (Hint: You will need to find the volume of two rectangular prisms each time.) a

3 cm

2 cm

b

1 cm

8 mm

4 cm

3 mm 2 mm

2 cm

7 cm

6m

c

5 mm

d

4 mm

3 mm

12 cm

30 cm

10 cm 8m 3m 3m 2m

8m

e

10 m

28 cm 10 cm 10 cm

8m 8m

f

45 m

32 m

g

cm

20 cm 1 cm

24

16 m

25

20 mm

50

cm

cm

45 mm

SkillBuilder 20-01 The cube

10 mm 50 mm

14 mm

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Using technology Spreadsheet

The volumes of rectangular prisms Using a spreadsheet, you can find the volume of a rectangular prism given its dimensions. Step 1: Set up the spreadsheet as shown. It will calculate the volume in cell D4. A 1

B

C

D

Volume of a rectangular prism

2 3

Length

Breadth

Height

4

Volume =A4*B4*C4

Step 2: Choose a value for the length to put in cell A4, a value for the breadth to put in B4 and a value for the height to put in C4. The volume automatically appears in D4. Step 3: Change the cells A4, B4 and C4 to the dimensions of another rectangular prism. The volume will change. Use your spreadsheet to answer Questions 1 and 3 in Exercise 11-04.

Working mathematically Applying strategies and communicating: What is your volume? Imagine that you are made up of rectangular prisms.

head

neck arms

torso

legs

feet

1 With the help of a partner, make measurements of your body. Use them to find dimensions (to the nearest centimetre) for each of the prism body parts. 2 Sketch each body part prism and label its dimensions. 3 Use the prisms to find your volume, in cm3. 4 Write a report of what you did, showing all diagrams and calculations. Explain how you found the dimensions (length, breadth and height) for the prisms. Do you believe you found a good approximation of your volume? Why?

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Working mathematically Applying strategies and reasoning: Packing sugar cubes Sugar cubes are sold in boxes of 100. Each sugar cube is 1 cm by 1 cm by 1 cm. You need to design the cheapest cardboard box to hold the cubes (that is, using the smallest amount of cardboard). One example is: 2 cm 5 cm 10 cm

However, this design does not use the smallest amount of cardboard. Draw your design for the box and explain how you decided that it was the cheapest design.

Capacity and liquid measure ‘What is the capacity of the water tank?’ Capacity is the amount of fluid (liquid or gas) in a container. The standard units of capacity are the litre (L) and the millilitre (mL). The same units are used to describe the volume of any liquid. A teaspoon holds about 5 mL. A tall standard carton of milk holds 1 L.

Unit millilitre litre kilolitre

Abbreviation mL L kL

Conversion 1 L = 1000 mL 1 kL = 1000 L

The diagram below will help you convert capacity units. × 1000

1 kL

× 1000

1 mL

1L

÷ 1000

÷ 1000

It is also useful to know the relationship between volume and capacity. 1 cm3 contains 1 mL 1 m3 contains 1000 L = 1 kL

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This means that a cubic centimetre can hold 1 mL of liquid, while a cubic metre can hold 1000 L of liquid.

1 mL

1 cm3

× 1 000 000 =

1 m3 = 1 kL = 1000 L

Just for the record Water, water, everywhere To help you better understand the size of a litre and a kilolitre, here are some examples of water use in and around the home: • Washing your hands/face uses 5 L • Brushing your teeth (tap running) uses 5 L • Brushing your teeth (tap not running) uses 1 L • Cooking and making coffee/tea uses 8 L per day • Flushing the toilet uses 9 L to 13 L • Flushing the toilet (half flush) uses 4.5 L to 6 L • Household tap uses 18 L per minute • Washing the dishes (hand) uses 18 L • Washing the dishes (dishwasher) uses 25 L per cycle • Bath uses 85 L to 150 L • Shower (8 minutes) uses 80 L to 120 L • Washing machine (front loading) uses 120 L per cycle • Washing machine (top loading) uses 180 L per cycle • Washing the car (with hose) uses 100 L to 300 L • Garden sprinkler uses 1 kL to 1.5 kL per hour • Garden hose uses 1.8 kL per hour • Swimming pool (backyard) uses 20 kL to 55 kL • Bradbury swimming pool (Olympic 50 m) uses 1870 kL On average, a four-person Sydney house (with garden) uses 936 litres of water per day. Half of it is used by outside taps or is flushed in a toilet. How much water does your household use each day? Find out by asking your parents to show you the water bill.

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Exercise 11-05 1 Find the capacity of: a a variety of milk containers c a standard soft drink can e the petrol tanks of a variety of cars g a petrol tanker

b d f h

2 Copy and complete: L a 7000 mL =

b 2L=

c

3 1--2-

e g i k m o

2500 mL = L L 4000 mL = mL 6.2 L = L 5 kL = L 25 000 kL = L 2.3 mL =

L=

mL

four different-sized soft drink bottles a standard cup your local swimming pool a small fruit juice pack mL

d 10 000 mL = f h j l n p

1.5 L = 8.5 L = 1750 mL = 9000 L = 520 mL = 6 mL =

L mL mL L kL L kL

3 Use this link to discover how Computer Algebra Software can be used to convert units of capacity. 4 Match the correct capacity (A to J) with the items (a to j) listed: a car petrol tank A 200 mL b liquid paper B 23 kL c bath tub C 5 mL d bucket of water D 70 L e can of drink E 1250 mL f glass of water F 1875 kL g Olympic swimming pool G 20 mL h bottle of lemonade H 7L i teaspoon I 375 mL j water storage tank J 180 L

CAS 11-02 Capacity and volume

5 A jug holds 2 L of water. How many 250 mL glasses could be filled from it? 6 James is inviting 30 friends to a party. He calculates that each person will drink 1800 mL of soft drink. a How many litres of soft drink must he buy? b James intends to buy large 2 L bottles of drink, how many bottles must he buy? 7 A bottle of medicine holds 100 mL. Tara was told to take 5 mL twice a day. For how many days can Tara take the medicine before it runs out? 8 A tap leaks 10 mL of water every 50 seconds. How much water will be lost in: a 1 second? b 1 minute? c 3 hours? d 1 day? 9 Your skin releases moisture as a way of controlling body temperature. On average 200 mL is released per hour. If all this moisture was captured, how long would it take to fill a 1.25 L soft drink bottle? VOLUME, MASS AND TIME

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10 A lunch box is made in the shape of a rectangular prism. Its dimensions are 20 cm, 15 cm and 9 cm. a Find the volume of the lunch box, in cm3. b How many mL of water would fit in the lunch box? 11 Jemma, the gardener, needs to purchase soil for her backyard. The dimensions of the yard are 15.2 m by 10.5 m. Find the volume of soil needed to cover the yard to a depth of 20 cm. (Note: The soil depth is in centimetres, not metres.) 12 Gina’s swimming pool is in the shape of a rectangular prism, 8 m long, 4 m wide and 1.5 m deep. a Find the volume of the swimming pool. b How many litres of water would be needed to fill the pool? (Hint: 1 m3 holds 1 kL.) 13 A fish tank in the shape of a rectangular prism is 60 cm long, 40 cm high and 30 cm wide. a Find the volume of the tank. b How many litres of water will it hold? 14 Use the words ‘volume’ and ‘capacity’ in sentences to clearly show their mathematical meaning. Then use them in sentences to show a different meaning for each one.

Working mathematically Applying strategies and reasoning: Volume by displacement Archimedes, an ancient Greek mathematician and inventor, discovered that the volume of an object fully immersed in a fluid equals the volume of the displaced fluid. (‘Displaced’ means moved from its position.) 1 Fill a measuring jug with 500 mL of water. 2 Choose at least five objects that can be safely immersed in the jug of water. 3 Copy and complete the following table for each object. Name of object

Original water level

Water level after putting object in

Difference in water level

Volume of object in cm3

500 mL 500 mL 500 mL 500 mL 500 mL

Remember: 1 mL takes up the same space as 1 cm3. 4 By placing a 1 cm cube in a medicine cup with water, show that a cubic centimetre displaces 1 mL of water. 5 By placing a cube with edges measuring 10 cm in a large measuring container, show that 1 L of water is displaced by the cube.

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Just for the record Minutes and seconds In Chapter 2, you learned that there are 360° in a revolution because the ancient Babylonians used a base 60 number system and believed that a year lasted 360 days. (How many days is a year actually?) The Babylonians, who lived where Iraq is today in 2000 BC, invented the units for measuring angles and time. That is why there are 60 minutes in an hour and 60 seconds in a minute. The word ‘minute’ has another meaning. When pronounced ‘my-newt’, it means tiny, but this meaning is also related to the minute as a unit of time. A minute is a tiny fraction of an hour, and comes from the Latin ‘pars minuta prima’, meaning the first division (or part) of an hour.

The word ‘second’ also means coming after first, and this meaning is also related to the second as a unit of time. Find out how.

SkillTest 11-01 Reading scales

Skillbank 11 Reading linear scales Understanding and reading the scale on a measuring instrument, on a number line or on the axis of a graph is an important mathematical skill. 1 Examine these examples. a Complete the missing values on the scale below. 100

120

140

160 km

• First, choose two values on the scale, say 100 and 120. • Count the number of intervals (‘spaces’) between the two values. There are four intervals between 100 and 120. • To find the size of each interval, divide the difference between the two values by the number of intervals: Difference = 120 − 100 = 20 km Number of intervals = 4 Size of an interval = 20 ÷ 4 = 5 km • Use the calculated size of an interval to complete the missing values: 100 105 110 115 120 125 130 135 140 145 150 155 160 km

b Complete the values on this scale. 50

• • • •

60

70

80

years

Choose 50 and 60 on the scale. Number of intervals (between 50 and 60) = 5 Difference (between 50 and 60) = 60 − 50 = 10 years Size of an interval = 10 ÷ 5 = 2 years. 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78

80 82 84 years

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2 Now copy and complete the following scales: a 36

40

44

48

52

56

60

64

°C

b 200

240

280

320

mL

360

c 500

520

540

560

g

580

d 128

144

cm

160

e 30

45

60

75

90

L

105

f 160

200

240

min

280

g 200

300

400

500

600

700

kg

h 12:00 midnight

6:00am

120

180

12:00 noon

6:00pm

240

300

12:00 midnight

6:00am time of day

i 360

420 seconds

j 100

200

300

400

500

600

700

mL

Mass You are asked to pick up: • a cubic metre of feathers

• a cubic metre of cement

You can lift the feathers but not the cement! The volume is the same but the mass is different. Even though they each take up the same amount of space, one is much heavier. Mass is the amount of matter in an object. The standard unit of mass is one kilogram (kg). Other units used are the milligram (mg), the gram (g) and the tonne (t). A drawing pin has a mass of about 1 g. An egg has a mass of about 60 g. A litre of water has a mass of exactly 1 kg. A medium-sized car has a mass of about 1.5 t.

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Unit milligram gram kilogram tonne

Abbreviation mg g kg t

Conversion 1 g = 1000 mg 1 kg = 1000 g 1 t = 1000 kg

The diagram below will help you convert units. × 1000

t

× 1000

× 1000

kg

÷ 1000

g

÷ 1000

mg

÷ 1000

Working mathematically Reflecting: Mass of household objects Each member of the group must find the mass of eight household objects. Taking it in turns, each person names the object and the rest of the group guesses its mass. Use a table like this: Object

My estimate

Actual mass

Difference

Check each guess against the actual mass and work out the difference between them. Did you get better at estimating by the end of the exercise? Why?

Exercise 11-06 Note: You will need a variety of weighing scales. 1 Measure the mass of: a this textbook c your schoolbag e a pencil case g a jumper i a ball (state what kind)

b d f h j

your lunchbox a shoe yourself a brick an apple

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2 Copy and complete: a 3000 g = kg g c 4 kg = e 7.5 t = kg g 2500 g = kg i 3800 kg = t CAS 11-03 Mass conversions

b d f h j

2t= kg 9000 kg = t 10 000 mg = g 1.5 kg = g 3g= mg

3 Use this link to discover how Computer Algebra Software can be used to convert units of mass. 4 Copy and complete, using a
,  or = sign to make each statement true: a 700 g 0.6 kg b 0.8 g 95 mg c 3500 kg 3.5 t d 1.7 kg 1700 g e 0.007 t 7 kg f 640 mg 0.7 g g 4000 mg 0.04 kg h 0.03 kg 3g 5 Match the masses given (A to J) with the items (a to j) listed: a an egg A 400 g b an elephant B 16 g c a house brick C 25 kg d a medium-sized car D 80 kg e an adult E 6t f a can of soft drink F 500 g g a 50c piece G 10 kg h a 7-year-old child H 50 g i a tub of margarine I 3 kg j a large watermelon J 1t 6 Measure the mass of 1 L of water. Write a report on how you did it. 7 Find out the difference between ‘gross mass’ and ‘net mass’. 8 Find out the difference between ‘mass’ and ‘weight’.

Working mathematically Applying strategies: Investigating mass 1 Investigate the sport of weight-lifting. 2 a Obtain a schedule of postal charges from the post office. Imagine that you have five pen-friends in different parts of the world (you choose the countries) and want to send a Christmas present to each one. Choose the presents. Work out the mass of each present when wrapped to send by post, and calculate the cost of sending each one by airmail and by sea. b Work out how much you will save by posting the presents early and sending them by sea. 3 Library research a Choose 10 animals and estimate their masses. Check your answers at the library. b Find 10 record achievements that have something to do with mass, for example heaviest man, lightest baby, etc.

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Timelines Timelines are the simplest types of calendars. They record events in the order in which they happen. A timeline for a puppy’s first 32 weeks could look like this: opened eyes

left mother

learnt to play fetch made a mess on the carpet

0

8

dug up new plants

ate a slipper

16

ate cake from table

Worksheet 11-04 History of the calendar

chased first cat

24

32 Weeks

You need to work out the scale used on the timeline before you can get information from it. On this timeline there are eight major divisions between 0 and 32, so each interval represents 4 weeks. Now you can see that, at 24 weeks, the puppy chased its first cat. It left its mother at about 6 weeks and at 20 weeks it started digging up the garden.

Exercise 11-07 1 a Copy this timeline.

3000 BC

2000 BC

1000 BC

1000 AD

b How many years does each interval on the timeline represent? (This is called the scale of the timeline.) c Write the following dates on the timeline in the correct boxes. AD 1 The birth of Christ The founding of the city of Rome 753 BC About 1600 BC Introduction of the current Chinese year system Start of the Mayan ‘Long Count’ 3111 BC Date recorded as the birth of Buddha 544 BC AD 1792 Declaration of the 1st French Republic AD 622 Traditional date for the flight of Muhammad VOLUME, MASS AND TIME

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2

G

C

A

1870

1770

F

B

1970 D

E

H

This timeline shows some events from the first 200 years of white settlement in Australia. a What is the scale of this timeline? b Match the letters on the timeline with these facts: 1851 Gold was discovered at Warrandyte, Victoria 1932 Sydney Harbour Bridge was opened 1974 Darwin was devastated by Cyclone Tracy 1956 Melbourne hosted the Olympic Games 1813 The explorers Blaxland, Wentworth and Lawson crossed the Blue Mountains 1788 The First Fleet arrived in Jackson Cove 1982 Brisbane hosted the Commonwealth Games 1901 The Federation of the Australian States to form the Commonwealth of Australia 3 The table below shows the names of Australia’s Governors-General and the year they each took office, from 1960 to 2001. Name

Year

A

Viscount Dunrossil

1960

B

Lord Casey

1965

C

Sir Zelman Cowen

1977

D

Viscount De L’Isle

1961

E

Right Reverend Dr Peter Hollingworh

2001

F

Sir William Deane

1996

G

Sir Paul Hasluck

1969

H

Sir John Kerr

1974

I

William Hayden

1989

J

Sir Ninian Stephen

1982

a Copy the timeline below and complete it by writing in the letters to indicate when each Governor-General took office. (Two have been done for you.) A

C

1960

1972

1984

1996

b What is the scale of this timeline? c Which Governor-General was in office for the longest period of time? d Which Governor-General was in office for the shortest time?

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2008

4 Draw a timeline to show these events for the period between 1945 and 2010: 1969 People first walked on the moon 1945 World War II ended 1989 Wayne Gardner won his first Australian 500 cc Motorcycle Grand Prix 19–– The year you were born 1985 The Aboriginal people were granted land rights to Uluru (Ayers Rock) 1964 The Beatles toured Australia 1983 Australia II won the America’s Cup 1956 The first television transmission in Australia occurred 1954 Englishman Roger Bannister was the first to run the mile in less than 4 minutes 2000 Olympic Games were held in Sydney 20–– (Enter your own important event.) 5 Draw a timeline to display these famous Australian inventions and discoveries: 1890 The Australian cattle dog was registered as the only purebred cattle dog in the world 1904 Kiwi Shoe Polish went on the market 1906 The surf-lifesaving reel for use at Bondi Beach was invented 1919 The preferential system of voting was first used for the House of Representatives 1922 Vegemite was developed by Dr Cyril Callister 1930 The world’s first mechanised letter-sorter was installed in the Sydney GPO, built by A. B. Corbett 1945 The Hills rotary clothes line was invented by Lance Hill 1952 The Victa rotary lawnmower was developed by Mervyn Victor Richardson 1979 Race-cam was first used by Channel Seven at the Bathurst 1000 car races 1983 The ‘Bionic ear’ cochlear implant came on the market 1988 Plastic banknotes, developed by the CSIRO, were first released 6 a Work with a partner or in a small group to write a list of important events that have occurred in your lifetime. Try to make a personal list. b Draw a timeline to show these events.

Working mathematically Communicating: Timeline display Work by yourself or with a partner to develop a poster or display showing a timeline for one of the following: • major disasters of the world • historical events of another country • achievements in science • achievements in sport • wars of the last 150 years • women in history • Prime Ministers of Australia • the history of computers • your school principals • a topic approved by your teacher. VOLUME, MASS AND TIME

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Converting units of time Example 4 1 Round each of these amounts of time to the nearest hour: a 7.83 hours b 12 hours 19 minutes c 2 hours 43 minutes 30 seconds

Solution a 7.83 h ≈ 8 h When rounding hours and minutes to the nearest hour, we use 30 minutes as the halfway mark because there are 60 minutes in an hour. For less than 30 minutes, round down and leave the number of hours unchanged. For 30 or more minutes, round up and add 1 to the number of hours. (because 19 min
30 min) b 12 h 19 min ≈ 12 h c 2 h 43 min 30 s ≈ 3 h (because 43 min  30 min) 2 Round each of these amounts of time to the nearest minute: a 11.4 minutes b 25 minutes 37 seconds c 3 hours 6 minutes 30 seconds

Solution a 11.4 min ≈ 11 min When rounding minutes and seconds to the nearest minute, we use 30 seconds as the halfway mark because there are 60 seconds in a minute. (because 37 s  30 s) b 25 min 37 s ≈ 26 min c 3 h 6 min 30 s ≈ 3 h 7 min (because we round 30 s up)

Example 5 1 Convert 7 minutes into seconds.

Solution so:

1 minute = 60 seconds 7 minutes = 7 × 60 seconds = 420 seconds

2 Convert 91 days into weeks.

Solution 7 days = 1 week 91 days = 91 ÷ 7 weeks = 13 weeks

so:

Example 6 Convert 275 minutes into hours and minutes.

Solution There are 60 minutes in 1 hour. 275 ÷ 60 = 4 remainder 35 275 minutes = 4 h 35 min

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NEW CENTURY MATHS 7

Most scientific calculators have a degrees-minutes-seconds key, ° ’ ” or DMS , that is useful for calculations involving minutes and seconds (base 60). This key can be used to convert decimal answers for time to hours-and-minutes or minutes-and-seconds. Calculating the answer to Example 6 in this way: 275 minutes = 275 ÷ 60 h = 4.583 333 3 … h Press ° ’ ” to get 4° 35′ 0″ on the calculator display, which means 4 h 35 min.

Exercise 11-08 1 State which unit of time (hours, minutes, or days) would be used to measure each of these events: a a day-night cricket match b snapping your fingers five times, as fast as possible c running once around the school oval d building a house e flying from Sydney to Broken Hill f watching a video from beginning to end g the life span of a grasshopper 2 Write these times correct to the nearest hour: a 4 h 14 min b 11.5 h d 7 h 48 min 19 s e 3.42 h

c 6 h 27 min f 2 h 30 min

3 Write these times correct to the nearest minute: a 17 min 51 s b 8.8 min d 4 h 20 min 19 s e 12.31 min

c 4 min 7 s f 1 h 28 min 40 s

4 Convert: a 6 hours to minutes c 9 weeks to days e 3 days to hours g 2 weeks to hours i 8.5 days to hours k 7.2 centuries to years 5 Convert: a 480 seconds to minutes c 96 hours to days e 468 weeks to years g 60 hours to days i 330 seconds to minutes and seconds k 135 minutes to hours and minutes m 405 minutes to hours and minutes 6 Find the number of seconds in: a 1 hour b 1 day

Example 4

Example 5

b d f h j

15 minutes to seconds 2.5 years to weeks 2 years to days 4.25 hours to minutes 10 1--2- minutes to seconds

l

3 fortnights to days Example 6

b d f h j l n

70 days to weeks 200 minutes to hours and minutes 560 seconds to minutes and seconds 126 days to weeks 24 weeks to fortnights 470 years to centuries 167 minutes to hours and minutes c 1 year

7 Are you over a million seconds old? Find your age in seconds to answer this question.

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Worksheet 11-05 Time calculations

Time calculations Example 7 What is the time 7 hours 40 minutes after 11:52pm?

Solution 7 hours after 11:52pm is 6:52am. 40 minutes after 6:52am is 7:32am.

Example 8 What is the difference in time between 8:35am and 3:10pm?

Solution From 8:35am to 9:00am = 25 minutes From 9:00am to 3:00pm = 6 hours From 3:00pm to 3:10pm = 10 minutes Total time difference = 25 min + 6 h + 10 min = 6 h 35 min or: Converting to 24-hour time first, then using the calculator’s 8:35am = 0835, 3:10pm = 1510 15

° ’”

10

–

° ’”

8

° ’”

35

° ’”

or

DMS

key:

=

° ’”

gives the display 6°35′0″ which means 6 h 35 min.

Example 9 Find 7 h 5 min − 3 h 24 min.

Solution

7 h 5 min − 3 h 24 min = 6 h 65 min − 3 h 24 min = (6 − 3) h + (65 − 24) min = 3 h 41 min or: Using the calculator’s ° ’ ” or DMS key: 7

° ’”

5

° ’”

–

3

° ’”

24

° ’”

=

gives the display 3°41′0″ which means 3 h 41 min.

Exercise 11-09 Example 7

1 What time will it be: a 5 hours after 3:00pm? c 28 minutes after 7:15pm? e 3 hours 19 minutes after 10:49pm? g 9 hours after 5:14pm? i 2 1--4- hours after 4:02am?

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NEW CENTURY MATHS 7

b d f h j

8 hours after 11:00am? 3 hours 32 minutes after 9:45am? 4 hours after 9:32am? 45 minutes after 3:30pm? 12 hours 40 minutes after 2:45am?

2 You may have discovered that it would be helpful to be able to count in time intervals. Use this link to go to an activity which enables you to practise counting time differences. 3 A marathon began at 10:20am. Here are some of the competitors and the times they ran: Mike 3:11 (3 h 11 min) Joe 2:23 Anna 2:54 Pathena 3:01 Ken 2:59 Gail 3:42 Write the runners in their order of finishing and the time each crossed the finishing line. 4 What is the difference in time between: a 7:15pm and 8:20pm? c 4:09am and 9:53am? e 7:27am and 1:12pm? g 7:45pm and 10:10pm? i 4:15pm and 6:02pm? k 8:40am and 4:19pm?

b d f h j l

5 Find: a 2 h 15 min + 4 h 32 min c 7 h 12 min + 5 h 18 min e 9 h 37 min + 2 h 52 min

b 3 h 25 min + 8 h 27 min d 1 h 42 min + 6 h 27 min f 4 h 49 min + 7 h 18 min

6 Find: a 6 h 42 min − 3 h 13 min c 15 h 57 min − 9 h 48 min e 8 h 18 min − 3 h 27 min

b 12 h 37 min − 5 h 6 min d 6 h 2 min − 4 h 17 min f 5 h 31 min − 3 h 48 min

10:16am and 12:06pm? 11:15pm and 3:08am? 9:36pm and 9:14am? 2:24am and 3:07am? 10:25am and 2:33pm? 6:45am and 8:10pm?

Spreadsheet 11-02 Counting with time

Example 8

Example 9

World standard times Worksheet 11-06 World time zones

Just for the record World time zones The world is divided into 24 main time zones. Time is the same throughout each zone. The centre of each time zone is a meridian of longitude (an imaginary line running from the North Pole to the South Pole). The meridians are 15° apart. The system used to divide the world was first suggested by Sir Sanford Fleming (1827–1915), a Canadian civil engineer and scientist. In 1884, scientists from 27 nations met in Washington and devised the time system we now use. Fleming was also responsible for a telegraph communication system. The first cable laid was between Canada and Australia in 1902.

Which major country uses only one time zone despite stretching across four time zones? VOLUME, MASS AND TIME

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The map below shows how times around the world are related. The Earth has been divided into standard time zones. Places within a time zone share the same time. All time is measured in relation to the time at Greenwich (in London), either ahead or behind Greenwich Mean Time (GMT). Australia’s time is ahead of Greenwich Mean Time since Australia is east of Greenwich. America’s time is behind Greenwich Mean Time since America is west of Greenwich. 180°W 150°W 120°W 90°W

60°W

30°W

0°

20°E

West of Greenwich (behind GMT)

60°E

90°E

120°E

150°E 180°E

East of Greenwich (ahead of GMT)

N

Greenwich Meridian Athens

International Date Line

New York

Beijing Hong Kong

Honolulu Equator

Rio de Janeiro

Greenwich Meridian

International Date Line

Helsinki Moscow Greenwich Geneva

Ottawa San Francisco

80°

12:00 2:00am 4:00am 6:00am 8:00am 10:00am 12:00 midnight noon

Sydney

2:00pm 4:00pm 6:00pm 8:00pm 10:00pm 12:00 midnight

2 From the given map, find the time in each of these cities when it is noon in Greenwich: a Sydney b Perth c New York d Beijing e San Francisco f Honolulu g Moscow h Geneva

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20° 0°

40°

60°

1 State whether each of these cities is ahead of or behind Greenwich Mean Time: a Sydney b Auckland c Rio de Janeiro d Perth e Beijing f Honolulu g Moscow h Athens i Hong Kong j Helsinki k New York l Ottawa

b d f h j

40°

20° Perth

Exercise 11-10

3 What is the time difference between: a Sydney and Perth? c Sydney and Honolulu? e Sydney and New York? g San Francisco and New York? i Geneva and Perth?

60°

Sydney and Beijing? Sydney and Moscow? Perth and Beijing? Honolulu and Moscow? San Francisco and Geneva?

4 If it is 2:00pm in Sydney, what is the time in: a Greenwich? b Perth? c New York? e San Francisco? f Honolulu? g Moscow?

d Beijing? h Geneva?

5 A cricket match being played in India is telecast live at 7:00pm Sydney time. What is the local time of the cricket match if Sydney’s time is 4 1--2- hours ahead of India’s? 6 Simone, in Newcastle, wants to use the Internet to chat with her cousin Zac in Vancouver, Canada. The time in Vancouver is 18 hours behind the time in Newcastle. At what time should Simone log on to the Internet to catch Zac when it is 3:00pm in Vancouver? 7 A plane leaves New Zealand at midday and takes 3 hours to fly to Brisbane. What is the local time in Brisbane when the plane lands, if Brisbane is 2 hours behind New Zealand? 8 Find out what happens if you cross the International Date Line (IDL). Why isn’t the IDL straight?

Working mathematically Applying strategies and reasoning: Round trip Plan a trip around the world with at least three stopovers. Obtain some airline timetables so you can give details of departures and arrivals. Work out how much time is actually spent flying. Does it matter if you head east or west when you start? What effect does the International Date Line have on your trip?

Australian standard times This map shows the time zones for Australia. Australian Western Standard Time (AWST)

Australian Central Standard Time (ACST)

Australian Eastern Standard Time (AEST)

Northern Territory Queensland Western Australia South Australia New South Wales Victoria

Tasmania

-2 hours

- 1 hour 2

Zero

Note: During daylight saving periods, add 1 hour. VOLUME, MASS AND TIME

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Exercise 11-11 1 State whether each location is ahead of, behind or has the same time as Adelaide: a Sydney b Melbourne c Darwin d Perth e Mt Isa (Qld) f Geraldton (WA) g Cobar (NSW) h Ceduna (SA) i Cairns (Qld) 2 What is the time difference between: a Sydney and Adelaide? b Melbourne and Perth? d Hobart and Darwin? e Canberra and Perth?

c Adelaide and Melbourne? f Brisbane and Canberra?

3 If it is 11:00pm in Sydney, what time is it in: a Melbourne? b Adelaide? d Darwin? e Hobart?

c Perth? f Canberra?

4 If it is 11:30pm in Adelaide, what time is it in: a Melbourne? b Sydney? d Darwin? e Hobart?

c Perth? f Brisbane?

5 a Find out when daylight saving begins and ends. b Why do we have daylight saving? c How does daylight saving affect the different time zones?

Worksheet 11-07 Tide chart

Timetables Exercise 11-12 1 Airline timetable Daniel and his volleyball team need to fly from Sydney to Brisbane for a championship tournament. Daniel logged on to the Internet site for Thomson Airways and found the following flight schedule for 12 October. Flight number

Sydney departure time

Brisbane arrival time

TH503 TH511 TH038 TH114 TH514 TH051

0905 0935 1005 1040 1105 1135

1030 1100 1130 1210 1230 1300

a How long does the flight take from Sydney to Brisbane? b The team would like to arrive at Sydney airport at 10:45am. How long will they need to wait for the next available flight? c The team needs to be at the hotel in Brisbane by 12:30pm. If it takes 30 minutes to drive from the airport to the hotel, what is the latest flight the team can catch from Sydney? d What is the flight number of the flight that takes longer to reach Brisbane than the others? Give one reason why it might take longer.

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NEW CENTURY MATHS 7

2 Bus Service Timetable Forward: Sydney to Wagga

Return: Wagga to Sydney

Sydney Strathfield Yagoona Liverpool Mittagong Goulburn* Yass Jugiong Gundagai Wagga

Wagga Gundagai Jugiong Yass Goulburn* Mittagong Liverpool Yagoona Strathfield Sydney

2:30pm 3:00pm 3:20pm 3:45pm 4:40pm 5:40pm 7:10pm 7:55pm 8:20pm 9:30pm

7:15am 8:25am 8:54am 9:41am 10:41am 12:10pm 1:05pm 1:20pm 1:35pm 2:05pm

* 30 minute meal stop at Goulburn

a b c d

How long does the trip from Sydney to Wagga take? How long would the trip take without a meal break? Ali joins the return bus at Jugiong and gets off at Liverpool. How long is his trip? Find the time taken from Liverpool to Sydney and from Sydney to Liverpool. Suggest a reason for the difference.

3 Countrylink Train Timetable Goulburn to Sydney — Monday to Friday GOULBURN MARULAN TALLONG WINGELLO PENROSE BUNDANOON EXETER MOSS VALE BURRADOO BOWRAL MITTAGONG YERRINBOOL BARGO TAHMOOR PICTON CAMPBELLTOWN STRATHFIELD SYDNEY

am

am

am

pm

pm

pm

pm

5:08 5:26 5:32

7:27 7:45 7:51

8:17

1:47

4:26

6:47

Bookings

Bookings

Bookings

Bookings

5:39

7:58

essential

essential

essential

essential

5:44 5:50 5:55 6:05 6:10 6:13 6:17 6:30 6:41 6:48 6:56 7:23

8:03 8:09 8:14 8:24

8:52

2:22

9:05

2:35

9:11 9:16

2:41 2:46

8:12

10:12

10:11 10:42 10:54

3:41 4:17 4:29

2:45 3:03 3:09 3:16 3:21 3:27 3:32 3:42 3:47 3:50 3:54 4:07 4:18 4:25 4:33 5:00

8:30 8:34

9:08 9:30

6:20

7:22 5:13

7:35 7:41 7:46

6:13 7:00 7:13

8:42 9:12 9:24

pm

7:45 8:03 8:09 8:16 8:21 8:27 8:32 8:42 8:47 8:50 8:54 9:07 9:18 9:25 9:33 10:00 11:04

a Michael has an interview in Sydney on Tuesday at 10:45am. At what time must he catch the train in Goulburn? b What is the difference in the time taken to travel from Goulburn to Sydney on the 5:08am train and the 8:17am train? c Georgina travels from Penrose to Yerrinbool, arriving at 4:07pm. How long did the trip take? d You have been visiting friends in Moss Vale and are returning to Sydney. Decide which train you would catch and explain why. e A new train is added to the timetable, leaving Goulburn at 11:12am. Write out a timetable for this train if it stops at the same stations as the 6:47pm train. VOLUME, MASS AND TIME

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4 The Explorer Bus The Explorer Bus operates in Sydney, Canberra and Melbourne. It takes tourists on a tour of the city and allows them to visit places of interest. This is a winter timetable for an Explorer Bus in a capital city: Depart Explorer depot City cathedral Railway station Parliament Museum City square Zoo Dockland shops Arts centre Water gardens Hall of fame Arrive Explorer depot

10:00 10:08 10:15 10:24 10:35 10:45 11:00 11:12 11:19 11:30 11:38

10:25 10:33 10:40 10:49 11:00 11:10 11:25 11:37 11:44 11:55 12:03

10:50 10:58 11:05 11:14 11:25 11:35 11:50 12:02 12:09 12:20 12:28

11:15 11:23 11:30 11:39 11:50 12:00 12:15 12:27 12:34 12:45 12:53

11:45 11:53 12:00 12:09 12:20 12:30 12:45 12:57 1:04 1:15 1:23

12:00 12:08 12:15 12:24 12:35 12:45 1:00 1:12 1:19 1:30 1:38

11:50 12:15 12:40

1:05

1:35

1:50

12:25 12:50 12:33 12:58 12:40 1:05 12:49 1:14 1:00 1:25 1:10 1:35 1:25 1:50 1:37 2:02 1:44 2:09 1:55 2:20 2:03 2:28 2:15

2:40

1:15 1:23 1:30 1:39 1:50 2:00 2:15 2:27 2:34 2:45 2:53 3:05

a How many buses are needed to meet the winter Explorer Bus timetable? Explain how you arrived at your answer. b Vo, Binh and Vicki came to the city by train, arriving at the station at 11:42am. They caught the Explorer Bus to the zoo. What is the earliest time they could expect to arrive at the zoo? Explain your answer. c Manuel and Sofia are dropped off by car at the ‘City cathedral’ at 10:25am. They arrange to meet their hosts at the ‘Hall of fame’ at 2:45pm. They want to spend at least half an hour at the museum, photograph the ‘City square’ and do some souvenir shopping at the Dockland shops. Plan a list of times for them to catch the Explorer Bus to do these things and meet their hosts on time. d In summer, extra Explorer tours leave the depot at 11:30am, 1:30pm, and 2:30pm. Make a list of departure times that would appear in the timetable for each of these tours.

Using technology Spreadsheet

The train timetable Use a spreadsheet to make up a timetable for a new railway line that runs trains on a route with nine stations. • Every third train runs express between stations 4 and 8. • Allow 2 to 4 minutes between each station. • Trains leave the first station every 15 minutes starting at 7:30am. • The last train leaves at 10:30am. • Give your stations creative names, or use the names of existing suburbs.

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NEW CENTURY MATHS 7

Working mathematically Applying strategies and reasoning: Time puzzlers Try to solve as many of the following puzzles as you can, on your own or in a group. Record your solution and how you solved the puzzle each time. Try the puzzles out on your family and friends.

Puzzler 1

If it takes 3 1--2- minutes to soft boil 1 egg, how long will it take to soft boil 3 eggs?

Puzzler 2 Here is a way to find someone’s age. Give them the following instructions. • Think of any number between 1 and 10. • Square it. • Subtract 1. • Multiply the result by the original number. • Multiply that by 3. • Add the digits of the answer. • Add your age in years and tell me the result. Now comes the trick: • First you need to guess the first digit of their age (that is, are they in their teens, 20s, 50s, etc.?). • Add the digits of the result you have been given. • Subtract the first digit of their age from this sum to get the second digit of their age.

Puzzler 3

The floral clock shown above gains half a minute during the day due to the warmth of the sun, and loses one-third of a minute during the cool of the night. If the clock was set to the correct time on 1 January, when will it be 5 minutes fast?

Puzzler 4 A doctor prescribed 15 pills and told his patient to take one every half-hour. How long would it take the patient to finish the course of pills? (Note: The answer is not 7 1--2- hours.)

Puzzler 5 Some months have 31 days, some have 30 days. How many months have 28 days?

Puzzler 6 How long is a metric hour if: 1 minute = 100 seconds and: 1 hour = 100 minutes?

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Power plus 1 The diagram on the right shows a tank. The tank is half-filled with water. Find the amount of water in the tank. 2 A cube has a volume of 512 cm3. Find the length of each side of the cube.

14 cm

15 cm 30 cm

3 A children’s pool is in the shape of a cross as shown on the right. Each side is 3 m long. The pool is filled with water to a depth of 300 mm. a Find the area of the pool surface. b Calculate the volume of water, in cubic metres (m3). c If water is charged for at $0.80 per kL, how much does it cost to fill the pool?

3m 3m

3m 3m

4 A doctor orders 5.2 litres of fluid each day to be given to a patient in drops. Each 1 mL of fluid is equivalent to 15 drops. How many drops of fluid per minute are needed for the patient to receive the required dose? 5 The diagram on the right shows a container in the shape of a rectangular prism. a How many cubes of side length 60 cm could be stacked in the container? b If each cube has a mass of 25 kg, how many tonnes would the container carry?

3m 3m

12 m

6 Calculate the volume of each solid below. a b

100 cm

8 cm

16 cm

2 cm 13 cm

13 cm 20 cm

8 cm

16 cm

16 cm

2 cm 30 cm

7 A rectangular box 40 cm long and 12 cm wide contains 2880 cm3 of sugar. How deep is the sugar in the box if it is spread evenly? 8 South Australia is 1 1--2- hours ahead of Western Australia. Anna is flying from Perth to Port Augusta. If the flight takes 2 1--2- hours and the flight leaves Perth at 10:00am on Sunday, at what time will the plane land in Port Augusta? 9 What happens if you travel east across the International Date Line? 10 If a 1 cm3 container can hold 1 mL, explain why a 1 m3 container can hold 1 kL.

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NEW CENTURY MATHS 7

Language of maths base cubic metre gram kilolitre milligram timetable 24-hour time

capacity Central Standard Time Greenwich Mean Time litre millilitre time zone volume

cubic centimetre Eastern Standard Time kilogram mass timeline tonne Western Standard Time

Worksheet 11-08 Measurement crossword

1 What is the difference between ‘volume’ and ‘capacity’? 2 Look up the different meanings of ‘capacity’ in the dictionary. How are these related to its mathematical meaning? 3 Find out the difference between a tonne and a ton. 4 What is a megalitre (ML)? 5 The word ‘minute’ can be pronounced differently and has different meanings. Find how the other meanings relate to a ‘minute’ meaning a fraction of an hour. 6 In Summer, the eastern states of Australia use AEDST instead of AEST. Explain.

Topic overview • Write in your own words what you have learnt about volume, about mass, and about time. • What parts of this topic were new to you? • What parts of this topic did you have difficulty with? Discuss them with a friend or your teacher. • Give some examples of situations where you would use what you know about volume, mass and time. • Copy this summary into your workbook and complete it. Use colour to help you remember your summary. Check it with other students and your teacher.

V _____ l×b×h

M _____ • mg •g • kg •t

cm3 m3

VOLUME, MASS and TIME 11

C _______ • mL •L • kL

12

1 2 10 9 3 T _____ ___ 4 8 7 6 5 VOLUME, MASS AND TIME

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Chapter 11 Ex 11-03

Review

Topic test Chapter 11

1 Count the cubes in this solid to find its volume:

Each cube = 1 cm3 Ex 11-04

2 Find the volume of each of these prisms: a 2m

b

4 cm 4 cm

5m 8m

20 cm

c

d

10 m

7 mm 6m

8 mm 12 mm 6m 15 cm

e 20 cm

f

6m

7m

10 cm

15 m 5m

15 m Ex 11-04

3 The biggest iceberg on record was called B9. It had the same volume as a rectangular prism with dimensions 160 km long, 50 km wide and 250 metres high. When B9 melted, how many litres of water was produced? (1 kL of water will occupy 1 m3.)

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NEW CENTURY MATHS 7

4 Copy and complete: L a 2000 mL = mL c 7L= L e 1750 mL =

b 3 kL = d 3300 L = f 2.5 mL =

5 The mass of an orange is closest to: A 5g B 50 g

C 500 g

Ex 11-05

L kL mL

Ex 11-06

D 5 kg

6 Eighteen trucks, each carrying 12 000 kg of debris, were required to clear a building site. How many tonnes of debris were cleared altogether?

Ex 11-06

7 Copy and complete: a 5000 g =

Ex 11-06

c 1 1--2- t =

kg

mg

d 6500 kg =

kg

e 4000 mg =

b 2g=

g

f

1.5 kg =

t g

8 Write each of these amounts of time correct to the nearest hour: a 9 h 50 min b 3.2 h c 4 h 12 min 49 s

Ex 11-08

9 Write each of these amounts of time correct to the nearest minute: a 2 min 36 s b 10.5 min c 3 h 23 min 40 s

Ex 11-08

10 Copy and complete: a 56 days = c 960 s = e 7 days =

Ex 11-08

weeks min h

b 4h= d 5 years = f 750 min =

min weeks h

11 What is the time: a 5 hours after 10:42pm? c 55 minutes before 7:15pm? e 15 hours 34 minutes after 7:00am?

b 2 hours 28 minutes after 5:23am? d 7 hours 36 minutes before 1:19am? f 3 1--4- hours after 3:40pm?

12 How much time elapses between: a 5.26am and 9:45am? c 1316 hours and 2003 hours? e 2347 hours and 0006 hours?

b 11:56pm and 7:30am? d 0750 hours and 1425 hours? f 1529 hours and 3:28pm?

13 Find: a 6 h 45 min + 3 h 20 min c 4 h 33 min + 2 h 24 min

b 3 h 16 min − 1 h 26 min d 4 h 19 min − 2 h 50 min

Ex 11-09

Ex 11-09

Ex 11-09

14 If it is 10:00am in Sydney, use the maps on pages 378 and 379 to help you work out the time in: a Perth b Rio de Janeiro c Adelaide d Moscow e Hong Kong f San Francisco

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Ex 11-10

CHAPTER 11