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8.07 Metric units for area and volume

Worksheet
Convert units of area
1

Identify the appropriate unit for measuring the following:

a

The area of a football field.

b

The area of a country.

c

The area of the face of a coin.

d

The area of an A4 sheet of paper.

2

Justin uses the conversion equation 1 metre = 100 centimetres to draw two squares with the same area:

a

Find the area of square A in \text{m}^2.

b

Find the area of square B in \text{cm}^2.

c

State the conversion equation from \text{m}^2 to \text{cm}^2.

3

Convert the following areas to \text{cm}^2:

a
6\text{ m}^2
b
4.2\text{ m}^2
c
0.8\text{ m}^2
d
7.92\text{ m}^2
4

Convert the following areas to \text{m}^2:

a
15\,000\text{ cm}^2
b
126\,000\text{ cm}^2
c
9000\text{ cm}^2
d
187\text{ cm}^2
5

Paul uses the conversion equation 1 kilometre = 1000 metres to draw two squares with the same area:

a

Find the area of square A in \text{km}^2.

b

Find the area of square B in \text{m}^2.

c

State the conversion equation from \text{km}^2 to \text{m}^2.

6

Convert the following areas to \text{ m}^2:

a
7\text{ km}^2
b
0.36\text{ km}^2
c
2.9\text{ km}^2
d
0.025\text{ km}^2
7

Convert the following areas to \text{km}^2:

a
4\,900\,000\text{ m}^2
b
980\,000\text{ m}^2
c
24\,500\,000\text{ m}^2
d
12\,000\text{ m}^2
8

The square shown in the diagram has an area of 1 \, \text{cm}^2:

a

Find its area in \text{mm}^2.

b

State the conversion equation from \text{cm}^2 to \text{mm}^2.

9

Convert the following areas to \text{cm}^2:

a
600\text{ mm}^2
b
35\,000\text{ mm}^2
c
5800\text{ mm}^2
d
81\text{ mm}^2
10

Convert the following areas to \text{mm}^2:

a
4\text{ cm}^2
b
22\text{ cm}^2
c
123\text{ cm}^2
d
6.2\text{ cm}^2
11

Convert the following areas as indicated:

a

5 \,\text{m}^2 to \text{cm}^2

b

6 \,\text{km}^2 to \text{m}^2

c

20\,000 \,\text{cm}^2 to \text{m}^2

d

1100 \,\text{mm}^2 to \text{cm}^2

e

12 \,\text{m}^2 to \,\text{cm}^2

f

11 \,\text{km}^2 to \text{m}^2

g

7 \,\text{cm}^2 to \,\text{mm}^2

h

7600 \,\text{cm}^2 to \text{m}^2

i

27\,000 \,\text{m}^2 to \,\text{km}^2

j

750 \,\text{mm}^2 to \,\text{cm}^2

k

10 \,\text{cm}^2 to \,\text{mm}^2

l

12\,500 \,\text{cm}^2 to \text{m}^2

m

1\,518\,000 \,\text{m}^2 to \,\text{km}^2

n

1520 \,\text{mm}^2 to \,\text{cm}^2

12

The following rectangle has side lengths given in centimetres:

a

Convert the dimensions of the rectangle into metres.

b
Hence find the area of the rectangle in square metres.
13

The following rectangle has side lengths given in millimetres:

a
Convert the dimensions of the rectangle into centimetres.
b
Hence find the area of the rectangle in square centimetres.
14

The following triangle has dimensions given in millimetres:

a
Convert the dimensions of the triangle into centimetres.
b
Hence find the area of the triangle in square centimetres.
15

Calculate the area of the following rectangles in square centimetres:

a

A rectangle with side lengths 0.16 \,\text{m} and 0.8 \, \text{m}.

b
A rectangle with side lengths 240 \, \text{mm} and 60 \,\text{mm}.
c
A rectangle with side lengths 22 \,\text{cm} and 0.9 \, \text{m}.
d
A rectangle with side lengths 22 \,\text{cm} and 90 \,\text{mm}.
16

Calculate the area of the following rectangles in square metres:

a

A rectangle with side lengths 0.018 \, \text{km} and 0.09 \, \text{km}.

b
A rectangle with side lengths 390 \text{ cm} and 12.5 \text{ m}.
17

Calculate the area of the following rectangles in square kilometres:

a

A rectangle with side lengths 2900 \,\text{m} and 600 \,\text{m}.

b
A rectangle with side lengths 470 \text{ m} and 6\,800 \text{ cm}.
18

John is tiling a room floor that has a total area of 9 \text{ m}^{2}. The tiles he is using are squares, measuring 25 \text{ cm} by 25 \text{ cm}.

a

Calculate the area of a single tile in square metres.

b

How many tiles will John require to cover the entire floor area?

19

A garden bed measures 430 \text{ cm} by 250 \text{ cm}. A bag of fertiliser covers an area of 2 \text{ m}^{2}.

a

How many whole bags of fertiliser are needed to cover the total area of the garden bed?

b

How much area will the left-over fertiliser be able to cover? Give your answer in square metres.

20

A sand pit set in the corner of a property has dimensions as shown:

a

Calculate the area of the sandpit in square metres.

b

A 20 \text{ kg} bag of play sand costs \$7.80, and covers an area of 0.5 \text{ m}^{2} to an appropriate depth.

How much will it cost to buy enough bags of sand to fill this sand pit?

Hectares
21

Convert 1 hectare to the following units:

a
\text{ m}^2
b
\text{ km}^2
22

Convert the following areas as indicated:

a

6 \,\text{ha} to \text{m}^2

b

2 \,\text{ha} to \text{m}^2

c

8.11 \,\text{ha} to \text{m}^2

d

10.7 \,\text{ha} to \text{m}^2

e

7.25 \,\text{ha} to \text{m}^2

f

26\,\text{ha} to \text{m}^2

g

26\,100 \,\text{m}^2 to \text{ha}

h

200\,000 \,\text{m}^2 to \text{ha}

i

84\,500 \,\text{m}^2 to \text{ha}

j

3\,200\,000 \,\text{m}^2 to \text{ha}

k

9\,750 \,\text{m}^2 to \text{ha}

l

16\,500\,000 \,\text{m}^2 to \text{ha}

23

Rectangular farms around Australia were measured and their dimensions are recorded in the table:

a

Complete the given table by calculating the area of each farm in \text{m}^2.

b

Which farm has an area of exactly 1 \, \text{ha}?

c

Which farms have an area of more than 1 \, \text{ha}?

d

Which farms have an area of less than 1 \, \text{ha}?

\text{Farm}\text{Length} \\\ \text{(m)}\text{Width} \\ \text{(m)}\text{Area} \\ \text{(m)}^2
1300100
235015
310020
435040
5100100
Convert units of volume
24

Identify the appropriate unit for measuring the following:

a

The volume of a match box.

b

The volume of an office building.

c

The volume of swimming pool.

d

The volume of sim card.

25

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

Find its volume in \text{mm}^3.

26

Convert the following volumes to \text{mm}^3:

a
5\text{ cm}^3
b
1.3\text{ cm}^3
c
0.08\text{ cm}^3
d
6.05\text{ cm}^3
27

Convert the following volumes to \text{cm}^3:

a
2000\text{ mm}^3
b
14\,000\text{ mm}^3
c
820\text{ mm}^3
d
26\text{ mm}^3
e
0.5\text{ m}^3
f
0.06\text{ m}^3
g
0.0075\text{ m}^3
h
6.05\text{ m}^3
28

Convert the following volumes to \text{m}^3:

a
90\,000\text{ cm}^3
b
2\,800\,000\text{ cm}^3
c
15\,000\,000\text{ cm}^3
d
126\,500\,000\text{ cm}^3
e
6\,000\,000\,000\text{ mm}^3
f
4\,000\,000\,000\text{ mm}^3
g
12\,000\,000\,000\text{ mm}^3
h
275\,000\,000\,000\text{ mm}^3
29

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

30

Find the volume of the following solid in cubic centimetres:

31

Find the volume of the following solids in cubic millimetres:

a
b
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Choose appropriate units of measurement for area and volume and convert from one unit to another

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