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1.07 Units of volume and capacity

Worksheet
Units of volume
1

Identify the appropriate unit for measuring the following:

a

The volume of a sand pit.

b

The volume of a match box.

c

The volume of an office building.

d

The volume of swimming pool.

e

The volume of sim card.

2

The cube shown in the diagram has a volume of 1\text{ cm}^3:

Find its volume in cubic milimetres.

3

Convert the following volumes to cubic milimetres (\text{mm}^3):

a
4 \text{ m}^3
b

3.5 \text{ cm}^3

c

4.2 \text{ m}^3

d

19 \text{ cm}^3

e
5\text{ cm}^3
f
1.3\text{ cm}^3
g
0.08\text{ cm}^3
h
6.05\text{ cm}^3
4

Convert the following volumes to cubic metres (\text{m}^3):

a
460\,000\,000 \text{ mm} ^3
b

51\,980\,000 \text{ cm}^3

c

1\,070\,000\,000 \text{ mm}^3

d
90\,000\text{ cm}^3
e
2\,800\,000\text{ cm}^3
f
15\,000\,000\text{ cm}^3
g
126\,500\,000\text{ cm}^3
h
6\,000\,000\,000\text{ mm}^3
i
4\,000\,000\,000\text{ mm}^3
j
12\,000\,000\,000\text{ mm}^3
5

Convert the following volumes to cubic centimetres (\text{cm}^3):

a

47\,600 \text{ mm}^3

b

8.12 \text{ m}^3

c

7000 \text{ mm}^3

d
2000\text{ mm}^3
e
14\,000\text{ mm}^3
f
820\text{ mm}^3
g
26\text{ mm}^3
h
0.5\text{ m}^3
i
0.06\text{ m}^3
j
0.0075\text{ m}^3
k
6.05\text{ m}^3
6

Convert the following as specified:

a

43\,\text{m}^3 to \text{cm}^3

b

18\,\text{cm}^3 to \text{mm}^3

c

12\,000\,000 \,\text{cm}^3 to \text{m}^3

d

9000 \,\text{mm}^3 to \text{cm}^3

e

8.97 \,\text{m}^3 to \text{cm}^3

f

9.77 \,\text{cm}^3 to \text{mm}^3

g

96\,900 \,\text{cm}^3 to \text{m}^3

h

92\,200 \,\text{mm}^3 to \text{cm}^3

Units of capacity
7

Identify the appropriate unit for measuring the following:

a

The capacity of a dose of vaccine injection.

b

The capacity of a bottle of washing detergent.

8

What metric unit represents one thousandth of a litre?

9

Convert the following to mililitres (\text{mL}):

a

6 \text{ L}

b

1.54 \text{ L}

c

0.5 \text{ kL}

d

0.025 \text{ kL}

e

21.3 \text{ L}

f

7.03 \text{ L}

g

1.05 \text{ kL}

h

0.009 \text{ kL}

10

Convert the following to litres (\text{L}):

a

5000 \text{ mL}

b

4920 \text{ mL}

c

1.67 \text{ kL}

d

10 \text{ kL}

e

420\,000 \text{ mL}

f

11\,080 \text{ mL}

g

96 \text{ kL}

h

200 \text{ kL}

11

Convert the following to kilolitres (\text{kL}):

a

8000 \text{ L}

b

6570 \text{ L}

c

950 \text{ L}

d

80 \text{ L}

e

70\,000 \text{ mL}

f

1\,850\,000 \text{ mL}

g

156\,000 \text{ mL}

h

1300 \text{ mL}

Converting between units
12

Convert the following to cubic centimetres (\text{cm}^3):

a

1 \text{ mL}

b

8000 \text{ mL}

c

40 \text{ mL}

d

4.47 \text{ mL}

e

22 \text{ kL}

f

0.09 \text{ kL}

13

Convert the following to litres (\text{L}):

a

6750 \text{ cm}^3

b

18.62 \text{ m}^3

14

Convert the following to cubic metres (\text{m}^3):

a

6000 \text{ L}

b

34 \text{ kL}

15

Convert the following to kilolitres (\text{kL}):

a

71.5 \text{ m}^3

b

7\,730\,000 \text{ cm}^3

16

Convert a volume of 72\ 000 \text{ cm}^3 to:

a

Litres (\text{L})

b

Kilolitres (\text{kL})

17

Convert the following as specified:

a

68\,000 \, \text{mL} to L

b

52 \,\text{L} to mL

c

99\,000 \,\text{L} to kL

d

63 \,\text{kL} to L

e

1 \,\text {cm}^3 to mL

f

1 \,\text{mL} to \text{cm}^3

g

36 \,\text {cm}^3 to mL

h

720\,\text{mL} to \text{cm}^3

i

1 \,\text{m}^3 to kL

j

1 \,\text{kL} to \text{m}^3

k

83 \,\text{m}^3 to kL

l

270 \,\text{ kL} to \text{m}^3

m

0.4 \,\text{L} to mL

n

3.8 \,\text{mL} to L

o

1.67 \,\text{kL} to L

p

84.6 \,\text{ L} to kL

Applications
18

Find the volume of the following solid in cubic centimetres:

19

Find the volume of the following solids in cubic millimetres:

a
b
20

A landscaper needs to move soil across the garden.

Approximately what capacity of soil can be carried by a wheelbarrow in one trip?

A
771 \text{ mL}
B
21 \text{ mL}
C
71 \text{ L}
21

Quiana bought a 400\text{ mL} bottle of soft drink. How many litres of soft drink did she buy?

22

This water bottle has a volume of 700 \text{ cm}^3.

a

Find its capacity in millilitres.

b

Find its capacity in litres.

23

This juice box contains 1600 \text{ mL} of juice.

a

Find its volume in cubic centimetres.

b

Calculate the length of the juice box if it is 8 \text{ cm} tall and 5 \text{ cm} wide.

24

A cubic box has capacity of 343\text{ L}. Find its volume in cubic centimetres.

25

A jug has a volume of 12\,395 \text{ cm}^3. How many litres of soda water can it hold? Round your answer to three decimal places.

26

A backyard pond can hold 12 \text{ m}^3 of water when full.

a

How many litres of water does the pond hold?

b

The garden hose has a flow rate of 40 \text{ L/min}. How long, in hours, will the pond take to fill from empty?

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Outcomes

ACMEM101

review metric units of volume, their abbreviations, conversions between them, and appropriate choices of units

ACMEM102

recognise relations between volume and capacity, recognising that 1cm^3 = 1mL and 1m^3 = 1kL

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