Chapter 16
Volumes
Volumes by Counting Cubes
1 cm3
The volume of a shape is the “amount of space” it occupies.
One unit of volume is the cubic centimetre.
1 cm
A cube which measures 1 cm by 1 cm by 1 cm and is written as 1 cm3 .
1 cm
1 cm
Exercise 16·1
1.
Each shape is made from 1 centimetre cubes.
3.
(a)
Write each volume in cm3 :–
(a)
Calculate the volume of each shape below :(b)
(b)
9 cm
5 cm
(c)
(d)
(c)
(d)
4 cm
(e)
(f)
12 cm
(e)
5 cm
2.
By working out the volume of the top layer,
calculate the total volume of each shape :–
(a)
(b)
4.
Calculate the volume of each cuboid below :–
(a)
2 cm
5 cm
12 cm
(b)
(c)
1 cm
8 cm
15 cm
Level EFT this is Chapter Sixteen
page 74
Volumes
Formula for the Volume of a Cuboid
To find the volume of a cuboid, you multiply the length x breadth x height.
Formula :–
Volume = L x B x H
Example :-
Find the volume of
the cuboid shown.
= LxBxH
Volume
1 cm
= 4x2x1
2 cm
= 8 cm3
4 cm
Exercise 16·2
1.
Copy and complete
to find the volume
of this cuboid :–
5.
6 cm
=
2.
2 cm
5 cm
... cm3 .
Find the volume of each cuboid below :–
(a)
6.
(b)
6 cm
3 cm
6 cm
(b)
1 cm
2 cm
1 cm
8 cm
2 cm
7 cm
1 cm
8 cm
3m
(c)
4·5 cm
7·2 m
5m
8·6 m
5·5 cm
8 cm
5·4 m
4 cm
Calculate the volume of each box :–
3 cm
(b)
15 cm
8 cm
5 cm
7.
40 cm
50 cm
4.
8 cm
6 cm
8 cm
5m
Chocolates
6 cm
4 cm
(a)
(d)
(a)
2 cm
Calculate the volume of each composite
shape below :–
1 cm
3.
2 cm
2 cm
1 cm
2 cm
(c)
2 cm
Find the volume
of each cuboid
and then find the
total composite
volume.
Volume = L x ... x ...
= 5 x ... x ...
A shape made from two or more shapes is
called a composite shape.
16 cm
12 cm
Five TeeJay books are stacked
on top of each other and the
pile measures 30 cm long by
21 cm wide by 7·5 cm high.
Find the missing dimension for each shape :–
(a)
Volume = 120 cm3
2 cm
6 cm
length
(b)
Find the volume of a stack
with only four books.
Volume = 60 cm3
height
2·5 cm
6 cm
Level EFT this is Chapter Sixteen
page 75
Volumes
Liquid Volume (Capacity)
If you take an open-top cube 1 cm by 1 cm by 1 cm
and fill it with water, we say it holds 1 millilitre of water.
Volume = 1 cm3
1 cm
= 1 ml
1 cm3 = 1 ml
1 cm
1 cm
Exercise 16·3
1. (a)
(b)
Calculate the
volume
of this
cuboidal
container, in cm3.
Remember :– to change from millilitres to litres
divide by 1000
4 cm
5 cm
4.
6 cm
Change each of the following to litres :–
How many millilitres
of liquid will it hold ?
(a)
5.
5 cm
10 cm
50 cm
(c)
12 cm
6 cm
7 cm
(c) 10 000 ml
(d) 8700 ml
(e)
(f) 54 200 ml
400 ml
(a) Calculate the
capacity
of this
cuboidal
50 cm
container in millilitres.
20 cm
50 cm
(b) How many litres of liquid will it hold ?
8 cm
5 cm
(b) 8000 ml
Remember :– 1000 cm3 = 1000 ml = 1 litre
2. How many millilitres of liquid will each of the
following containers hold ?
(b)
(a) 4000 ml
6.
16 cm
Calculate how
many litres this
container holds.
20 cm
30 cm
(d)
40 cm
35 cm
7.
80 cm
How many litres will each of the following
containers hold ?
(a)
125 cm
(b)
5 cm
40 cm
3. Volume can also be measured in cubic metres.
50 cm
Calculate the volume of each of these shapes in m3 .
(a)
(b)
2m
3m
3m
5m
3m
80 cm
10 cm
25 cm
(c)
80 cm
3m
100 cm
500 cm
(c)
50 (cm)
12 m
(d)
2 cm
2m
10 cm
86 cm
Level EFT this is Chapter Sixteen
page 76
Volumes
8.
How many litres
of water will this
container hold
when :–
10. A small 2 litre jug is used to fill the tank below.
10 cm
50 cm
80 cm
(a) full
(b) half full
80 cm
40 cm
(c) 30% full ?
9.
120 cm
A cuboidal glass aquarium has a length of
50 centimetres and breadth of 40 centimetres.
(a) How many full jugs are needed to fill the
tank ?
If 30 litres of water are poured into the
aquarium it will be half full.
When the tank is full, the tap is opened and
water pours out at 3 litres every 30 seconds.
Calculate the height of the aquarium.
(b) How many minutes will it take for the tank
to empty ?
What Have I Learned ?
1.
Write the volume of each shape in cm3 :–
4.
Calculate the volume of the cuboid below.
0·5 m
(a)
10 m
16 m
5.
This cuboid has a
volume of 120 cm3 .
height
(b)
Calculate the height.
6.
(c)
7.
10 cm
20 cm
How many litres of water would it take to
fill the cuboid below ?
20 cm
Use the formula
to calculate the
volume of the
cuboid shown.
30 cm
50 cm
400 cm
20 cm
8·5 cm
3.
(a) Calculate the
volume of this
cuboid in cm3 .
(b) Write down its
30 cm
capacity in millilitres.
4 cm
2.
5 cm
6 cm
8.
Find the volume of a cube with side 5 cm.
Level EFT this is Chapter Sixteen
(Hard) 100 litres of water are poured into an
open-topped cube of side 50 centimetres.
Find the depth of water in the cube.
page 77
Volumes