Shape and Space - part 1
V OLUMES C UBES A ND C UBOIDS 1
The space taken up by a 3D shape is called its volume.
Volume is measured in cubic units, such as cubic centimetres (cm ³ or cc) and cubic metres (m ³ )
A cubic centimetre looks like this
A cubic metre could be the size of a large tank.
100cm
100cm
100cm
A cubic metre measures 100cm in each direction.
CUBES AND CUBOIDS
Each of the cubes in this shape is one cubic centimetre
How many cubic centimetres are there altogether?
There are 3 rows of 4 cubes, 1 layer deep.
3 x 4 x 1 = 12cm ³ x le i p acks
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Shape and Space - part 1
In this block the top layer has 3 rows of 4 cubic centimetres.
But there are 2 layers.
Altogether there are : 3 x 4 x 2 cubic centimetres
= 24cm ³
So to find the volume, count the blocks in the top row and multiply by the number of layers.
Volume = length x width x height
 top row
 number of layers
Try these questions:
3)
How many cubic centimetres are there in these cuboids?
1) 2)
4)
Check your answers, then discuss with your tutor what you need to work on next.
2 x le i p acks

Shape and Space - part 1
5)
7)
8)
6) x le i p acks
3

Answers
Volumes Cubes And Cuboids 1
1) 12cm
³
2) 20cm ³
3) 30cm ³
4) 27cm
³
5) 36cm ³
6) 64cm
³
7) 125cm ³
8) 120cm ³
Shape and Space - part 1 x le i p acks
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Shape and Space - part 1
V OLUMES C UBES A ND C UBOIDS 2
To find the volume of a cube/cuboid, multiply: length x width x height
Example:
What is the volume of a child’s shoe box 20cm long, 10cm wide and
8cm high?
Volume = length x width x height
= 20 x 10 x 8cm
= 200 x 8cm ³
³
= 1600cm ³
Note - the volume of an empty shape may be called the cubic capacity.
A) Try finding these volumes (the answers will be in cubic units eg cm ³ , m ³ etc)
1)
5m
3m
3m
2)
3cm
2cm
9cm x le i p acks
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Shape and Space - part 1
3)
5)
5m
5m
4)
5m
6cm
18cm
5cm x le i p acks
10cm
6
9cm
20cm

Shape and Space - part 1
6) A ring case measures 3cm by 3cm and is 2cm high. What is it’s volume in cm ³ ?
7) A square shaped tube is 85cm high, and has a length and width of
5cm each way. What is it’s capacity?
8) A room in a club is 9m wide, 26m long and 4m high. What is it’s volume?
9) A car radio speaker is 18cm wide, 9cm deep and 10cm high. What volume is it?
10) A plant container is in the shape of a cube with a side length of
9cm. What capacity does it have?
11) Joanne thinks a cube with sides of 8cm holds more than a cuboid with sides of 6, 8 and 10cm. Is she right?
LONG MULTIPLICATION AND DECIMAL FRACTIONS
You may need to do long multiplication.
Example:
What is the volume of a box with dimensions 35cm by 25cm by 8cm?
Multiply length x width 35 x 25
175
700
875
 don’t forget the 0
Now multiply by the height 875
x 8
7000
Answer = 7000cm ³ x le i p acks
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Shape and Space - part 1
You may have to multiply decimal fractions.
Example:
A room is 5.6m long, 4m wide and 3m high. What is it’s volume? length x width 5.6
x 4 x height 22.4
x 3
22.4
2
67.2
1
The volume is 67.2m
³
B) Try these questions.
1) A baking tray measures 25cm x 30cm x 5cm. What is it’s volume in cm ³ ?
Another tray measures 25cm by 25cm by 6cm. Which tray holds more?
2) Find the volume of these jewellery cases, in cubic centimetres.
Length Width Height
◘ a) 4cm b) 6.2cm
2cm
3cm
3.5cm
5cm c) 5.5cm 8cm 14cm
3) What is the volume of a Weetabix packet which measures 25cm by 20cm by 5cm?
4) What is the volume of a matchbox which measures 11cm by 6.4cm by 3cm? x le i p acks
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Shape and Space - part 1
5) Small boxes measuring 3cm by 2cm by 1cm are packed into a large box which measures 15cm by 12cm by 10cm. What is the volume of: a) the small boxes? b) the large box? c) How many small boxes will fit into the large box?
6) Ice cubes which measure 2cm by 2cm by 2cm are made with water from a container 16cm by 13cm by 8cm. How many can be made?
7) Crates which measure 1.5m by 2m by 2m are packed in a large container 9m by 4m by 3m. How many can be packed in?
You may need to do long multiplication with a decimal fraction.
Example:
A shoulder bag is 8.5cm by 21cm by 9cm. What is it’s cubic capacity?
85 x 21
85
1700
1785
8.5  1 decimal place x 21
85
1700
178.5  1 decimal place
178.5
x 9
1606.5
7 7 4
Answer = 1606 5cm ³ x le i p acks
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Shape and Space - part 1
C) Try finding these volumes.
1) What is the volume of these music speakers?
Length Width a) 25cm b) 18.2
20cm
16cm
Height
35cm
30cm c) 9cm 9.5 15cm
2) Nina is checking on the cubic capacity of different freezing compartments in fridges.
The first model has a compartment measuring 9.5cm by 30cm by
40cm.
The second compartment measures 21.5cm x 18cm x 30cm.
Which has the larger capacity?
Check your answers, then discuss with your tutor what you need to work on next. x le i p acks
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Shape and Space - part 1
Answers
Volume Cubes And Cuboids 2
A)
1) 45m
³
B)
1) 3750cm ³
2) 54m ³
3750cm ³ same
3) 125m ³
4) 540cm
³
5) 1800cm ³
2) a) 28cm ³ b) 93cm ³ c) 616cm
³
6) 18cm
³ 3) 2500cm ³
7) 2125cm ³ 4) 211.2cm
³
8) 936m ³
9) 1620cm
³
5) a) 6cm ³ b) 1800cm
³ c) 300
10) 729cm ³
6) 1664

8 = 208 ice cubes
11) 512cm
³
480cm ³
She is right
7) 108

6 = 18 crates
C)
1) a) 17500cm
³ b) 8736cm ³ c) 1282.5cm
³
2) 11400cm
³
11610cm ³ the second x le i p acks
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Shape and Space - part 1
V OLUMES C UBES A ND C UBOIDS 3
Volume = length x width x height
V = l w h
When you use measurements with decimal fractions, just remember the rules for multiplying decimals.
Example:
To find a volume 3.2cm by 2.8cm by 1.5cm
32 x 28
256
640
896
32 x 28 = 896
3.2 x 2.8 = 8.96
(3.2 has 1 decimal place and
2.8 has 1 decimal place -
2 decimal places altogether)
896 x 15
4480
8960
13440
896 x 15 = 13440
8.96 x 1.5 = 13.440
(8.96 has 2 d.p. and 1.5 has
1 d.p. - 3 decimal places altogether)
Answer = 13.44cm
³ (Check this is sensible - we started with 3.2 x 2.8 x 1.5. 3 x 2 x 1 = 6 so 13.44 is reasonable)
A) Try these questions.
Find the cubic capacity of these rooms (to 2 decimal places if necessary)
Length Width Height
1) Hall
2) Living room
2.5m 2.5m 3.2m
4.4m 3.6m 3.2m x le i p acks
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Shape and Space - part 1
3) Bedroom
4) Bathroom
4.5m
3.5m
3.8m
3.2m
2.5m
2.5m
PROBLEM VOLUMES
You may know the volume but need to find a missing measurement.
Example:
A biscuit tin has a volume of 1800cm ³ . The length is 30cm, the width is 15cm. What height is it? length x width = 450cm
15cm
30cm
?
Divide this into the volume to find the height:
1800  450 = 4
The height is 4cm
B)
1) A 12cm square cake tin is used to make a cake 2cm high. What is the volume of the cake?
If a different , rectangular tin is used, 12cm long and 8cm wide, what will be the height of the cake?
2) A box needs to have a cubic capacity of 2000 cubic centimetres.
If the base is to be 25cm by 10cm, how high will the box need to be?
3) Kathie has 5000 cubic centimetres of concrete mix. She wants to fill a space 5cm high and 50cm long. What width can she cover?
13 x le i p acks

Shape and Space - part 1
CAPACITY
It is useful to know that 1 litre is the same as 1000 cubic centimetres
(cm ³ or cc for short) - as in engine size; a 2 litre engine is 2000cc.
1 litre

 has a volume of 1000cm ³ has a liquid capacity of 1000 millilitres
So when we measure a volume we can also work out the liquid capacity.
Example:
This paddling pool is 120cm by 120cm.
It is 30cm high. If it's filled to the top, its capacity is 120 x 120 x 30cm ³ .
There are 1000cm ³ in a litre, so it can hold:
120 x 120 x 30 litres
1000
Cancel the 0’s: 120 x 120 x 30 litres
1000
= 12 x 12 x 3 litres
= 432 litres
(If you are not sure about cancelling fractions, just multiply
120 x 120 x 30 = 432000 then divide by 1000 = 432 litres)
C) Try these questions:
1) This paddling pool is filled to a depth of 20cm. How many litres are needed to fill it?

20cm

100cm
120cm
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Shape and Space - part 1
2) Two toddlers have a pool which measures 50cm by 50cm and is
10cm deep. They have buckets which hold 1 litre of water. How many times will they have to refill the buckets to fill the pool?
3) John grows tomatoes in his greenhouse and waters them regularly. They need at least half a litre of water each time. His water tank measures 40cm x 50cm and is 120cm high. How many plants can be watered from a full tank?
Check your answers, then discuss with your tutor what you need to work on next. x le i p acks
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Answers
Volumes Cubes And Cuboids 3
A)
1) 20m ³
2) 50.688m
³
3) 42.75m
³
4) 28m ³
B)
1) 288m
³
288

96 = 3cm high
2) 2000

250 = 8cm high
3) 5000

250 = 20cm
C)
1) 240 000

1000
= 240 litres
2) 25000cm ³ = 25 litres
25 times
3) 240 000cm
³ = 240 litres
480 plants x le i p acks
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Shape and Space - part 1