topic badge
CanadaON
Grade 7

10.05 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.

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?

Convert units of volume
21

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.

22

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

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

23

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
24

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
25

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
26

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

27

Explain how to find the volume of the following solid in cubic centimetres.

28

Find the volume of the following solids in cubic millimetres:

a
b
Sign up to access Worksheet
Get full access to our content with a Mathspace account

Outcomes

7.E2.1

Describe the differences and similarities between volume and capacity, and apply the relationship between millilitres (mL) and cubic centimetres (cm^3) to solve problems.

7.E2.2

Solve problems involving perimeter, area, and volume that require converting from one metric unit of measurement to another.

What is Mathspace

About Mathspace