Volume
Volume
Volume is the amount of space
occupied by any 3-dimensional (3D)
object.
The units for volume are…
mm3, cm3, m3 and km3
Units of Volume
When we measure volume we find how many
cubes it would take to fill a space.
1mm
1mm
1mm
= 1 mm3 (1 millimetre cubed)
1cm
1cm
1cm
= 1 cm3 (1 centimetre cubed)
1m
= 1 m3 (1 metre cubed)
1m
1m
Volume by Counting
If each cube
measures 1 cm3 find
the Volume
6 cm3
1cm
1cm
1cm
If each cube measures
1 cm3 find the Volume
1cm
1cm
1cm
12
3
cm
If each cube measures
1 cm3 find the Volume
1cm
1cm
1cm
32
3
cm
If each cube measures
1 cm3 find the Volume
1cm
1cm
1cm
27
3
cm
If each cube measures
1 cm3 find the Volume
1cm
1cm
1cm
15
3
cm
Volume of Cuboids using
a formula
What is a
Cuboid?
Top
Side 2
Back
Front
Bottom
Side 1
Height (H)
Width (W)
Length (L)
A 3D
rectangle
Volume
Volume
of a Cuboid
All this counting will take a long
3 row
you
a quicker
waylayer.
to
4time.
rowsCan
of 5
5cm
cm33see
=in20cm
each
in each
find the volume?
4 cm
3
40
cm
60 cm3
5 cm
Volume = 5 x 4 x 3 = 60 cm3
3cm
Volume of Cuboid
Formula
It takes far too long to count
cubes so lets use a formula…
Volume = Length x Width x Height
h
l
w
V=lxwxh
http://www.youtu
be.com/watch?v=
TxAi3J_LlzA
(still stuck?: go to
above link)
Find the volume of this
cuboid
This cuboid measures
2cm by 2cm by 3cm so
the volume is …
V = 2 x 2 x 3 = 12cm3
Check by counting
Find the volume of this
cuboid
This cuboid
measures 4cm by
4cm by 2cm so
the volume is …
V=4x4x2=
32
3
cm
Check by counting
Find the following Volumes
4 mm
36 mm3
Volume = 2 cm x 7 cm x 6 cm
= 84 cm3
84 cm3
7 cm
4m
36 mm3
3 mm
3 mm
2 cm
Volume = 4 mm x 3 mm x 3 mm
= 36 mm3
84 cm3
6 cm
Volume = 9 m x 4 m x 6 m = 216 m3
216 m3
216 m3
6m
9m
What is a
Cube?
Square Side
Square Top
Square
Back Square
Side
Square
Front
Square
Bottom
Length (L)
Length (L)
Length (L)
A 3D square
Volume of a Cube Formula
L
L
L
• Volume = Length x Length x Length
=LxLxL
= L3
If the length of each
cube measures 1 cm find
the Volume
1cm
Volume = 2 x 2 x 2 =
1cm
1cm
Find the volume of the following cuboids.
4 cm
1
Volume = 4 x 4 x 4 = 64 cm3
Volume = 5 x 5 x 5 = 125 cm3
3
2
3m
5m
Volume = 3 x 3 x 3 = 27 m3
Time for a silly song.
http://www.youtube.com/watch?v=A2WsSHf96sQ
Prisms
SLO: Know the names of the
parts of 3D shapes
Edge
Face
Vertex
What is a Prism?
Cylinder
Cuboid
What do they all
Uniform
section
have incross
common?
Trapezoid Prism
Triangular Prism
http://www.youtube.com/watch?v=gSJtOUgFS-0
(what is a prism video)
Which of the following
shapes are prisms?
Volume of Prism Formula
Volume of Prism = Cross-sectional area x length
Length
Your Turn: Volume of Prism
Area = 10 cm2
8 cm
Volume = Cross Sectional Area x Length
= 10 x 8
= 80 cm3
http://www.youtube.com/watch?v=
6nJgDehGmI4
(video to find volume of any prism)
Your Turn: Volume Cuboid
Cross-sectional Area = b x h
=7x5
= 35 cm2
5cm
10cm
7cm
Volume = Cross Section Area x Length
= 35 x 10
= 350
3
cm
Your Turn:
Volume Triangular Prism
Cross-sectional Area = ½ x b x h
=½x8x4
= 16 cm2
4cm
4.9cm
10cm
8cm
Volume = Cross Section Area x Length
= 16 x 10
= 160 cm3
http://www.khanacademy.org/math/geometry/basicgeometry/v/solid-geometry-volume
(Khan: how to find volume of triangular prism)
Your Turn:
Volume Cylinder
Cross-sectional Area = π x r2
3cm
= π x 32
= 27cm2 (I have used π = 3)
5cm
Volume = Cross Section Area x Length
= 27 x 5
= 135 cm3
(Liquid volume)
(fluid ounce)
cup
(pint)
millilitre
litre
(quart) (gallon)
http://www.youtube.com/watch?v=WmLi9ydZmA (video: what is capacity)
Comparing ml, L and
1 ml
1cm
1cm
= 1 ml
(1 cm3 = 1 ml)
1cm
1 Litre
10 cm
10 cm
10 cm
3
cm
= 1 litre
(1000 cm3 = 1L)
Converting between cm3 and Litres
Divide by 1000
Move the number 3
places to the right
when dividing by
1000.
Litre
3
cm
Multiply by 1000
Move the number 3 places
to the left when
multiplying by 1000.
E.g.
Fill in the table below
cm3
Litre
1)
2000
2
2)
4000
4
3)
5780
5.78
4)
540
0.54
Extension Activity
http://www.youtube.com/watch?v=eGVi37wFeZU
Thanks
This power point has been put together
using power points, images, videos and
games from the net.
Thank you to all those who have placed
their work in the public domain. For
others to use.