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2.07 Units of volume and capacity

Worksheet
Estimation
1

Consider the matchbox shown:

a

State the most appropriate unit for measuring the volume of a match box.

b

Estimate the volume of the matchbox.

2

The volume of the suitcase shown has a total capacity of 88\,500\text{ cm}^3.

Estimate the volume of the contained shirts.

3

The volume of the bookshelf shown is known to be 0.68\text{ m}^3 .

Estimate the volume of the books on the bookshelf.

4

The volume of the bookshelf shown below is known to be 0.64 \text{ m}^{3}.

Estimate the volume of the books on the bookshelf.

5

Estimate the volume of liquid in this container if it is able to hold 2400 \text{ mL} when full.

6

Estimate the volume of liquid in this container if it is able to hold 3.6\text{ L} when full.

7

Estimate the volume of liquid in this container if it is able to hold 3600\text{ mL} when full.

8

Estimate the volume of liquid in this container if it is able to hold 3.8 litres when full.

9

A landscaper needs to move soil across the garden. Choose the best estimate for the capacity of soil that can be carried by a wheelbarrow in one trip.

A
771\text{ mL}
B
21\text{ ML}
C
71\text{ L}
Units of volume
10

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.

11

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

Find its volume in cubic milimetres.

12

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
13

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
14

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
15

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
16

Identify the appropriate unit for measuring the following:

a

A small carton of milk.

b

A dose of vaccine injection.

c

Water in a dam.

d

A cup of coffee.

e

A large bottle of washing detergent.

f

The Atlantic Ocean.

17

What metric unit represents one thousandth of a litre?

18

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}

19

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}

20

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
21

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}

22

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

a

6750 \text{ cm}^3

b

18.62 \text{ m}^3

23

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

a

6000 \text{ L}

b

34 \text{ kL}

24

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

a

71.5 \text{ m}^3

b

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

25

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

a

Litres (\text{L})

b

Kilolitres (\text{kL})

26

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
27

Find the volume of the following solid in cubic centimetres:

28

Find the volume of the following solids in cubic millimetres:

a
b
29

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

30

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

a

Find its capacity in millilitres.

b

Find its capacity in litres.

31

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.

32

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

33

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.

34

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

3.1.4.1

use metric units of volume (cubic millimetres, cubic centimetres, cubic metres), their abbreviations (mm^3, cm^3, m^3), conversions between them and appropriate choices of units

3.1.4.2

understand and use the relationship between volume and capacity, recognising that 1 cm3 = 1 mL (millilitre), 1000 cm3 = 1 L (litre), 1 m3 = 1 kL (kilolitre), 1000 kL = 1ML (megalitre)

3.1.4.3

estimate volume and capacity of various objects

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