Volume - Gore High School

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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
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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.
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