Volume
S4
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Counting Volume cubes
Volume of a cuboid
Liquid Volumes
Volume of cylinder
Volume of triangular prism
30-Nov-11 Compiled by Mr. Lafferty Maths Dept.
S4 Starter Questions
S4
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30-Nov-11 Compiled by Mr. Lafferty Maths Dept.
Volumes by Counting Cubes
S4
Learning Intention Success Criteria
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1. To understand the 1. To know what volume
term volume in terms of means.
counting cubes.
2. Work out volumes using
3
1cm cubes.
3. Answer to contain
appropriate units.
30-Nov-11 Compiled by Mr. Lafferty Maths Dept.
Volumes by Counting Cubes
S4
Volume is the amount of space a 3D - shape takes up
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1cm
1cm
One Unit of Volume is the “CUBIC CENTIMETRE”
= 1 centimetre cube = 1 cm³
30-Nov-11 Compiled by Mr. Lafferty Maths Dept.
Volumes by Counting Cubes
S4
This shape is made up of 1 centimetre cubes placed
next to each other. What is its volume in cm³?
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1cm
1cm 1cm
= 2 centimetre cubes = 2 cm³
30-Nov-11 Compiled by Mr. Lafferty Maths Dept.
Volumes by Counting Cubes
S4
This shape is made up of 1 centimetre cubes placed
next to each other. What is its volume in cm³
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1cm
1cm 1cm
= 3 centimetre cubes = 3 cm³
30-Nov-11 Compiled by Mr. Lafferty Maths Dept.
Volumes by Counting Cubes
S4
What is its volume in cm³ of these shapes.
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3
5 cm
3 3
5 cm 6 cm
30-Nov-11 Compiled by Mr. Lafferty Maths Dept.
Volumes by Counting Cubes
S4
One unit of Volume is the “CUBIC CENTIMETRE”
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3cm
4cm
Volume = 24 centimetre cube
= 24 cm³
30-Nov-11 Compiled by Mr. Lafferty Maths Dept.
Volumes by Counting Cubes
S4
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Now try Ex 1
Ch8 (page 89)
30-Nov-11 Compiled by Mr. Lafferty Maths Dept.
S4 Starter Questions
S4
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Student Discount
⅓ off the price of each pizza
30-Nov-11 Compiled by Mr. Lafferty Maths Dept.
Volume of a cuboid
S4
Learning Intention Success Criteria
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1. To understand how to 1. To know the formula.
calculate the volume
of cuboid.
2. Use formula correctly.
3. Show working and
appropriate units.
30-Nov-11 Compiled by Mr. Lafferty Maths Dept.
Volume of a cuboid
S4
18 cubes fit
the base.
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4cm
3cm
6cm
= 1 centimetre cube = 1 cm³
4 layers of 18 cubes
= 4 x 18 = 72 centimetre cubes = 72 cm³
30-Nov-11 Compiled by Mr. Lafferty Maths Dept.
A short cut !
S4
height
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4cm
Area of
rectangle
3cm breadth
6cm
length
Volume = 6 x 3 x 4 = 72 cm³
Volume = length x breadth x height
30-Nov-11 Compiled by Mr. Lafferty Maths Dept.
Example 1 Working
S4
Volume = l x b x h
V = 18 x 5 x 27
V = 2430 cm³
27cm
Heilander’s
Porridge Oats
18 cm
30-Nov-11 Compiled by Mr. Lafferty Maths Dept.
Example 2
Working
S4
Volume = l x b x h
V=2x2x2
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V = 8 cm³
2cm
30-Nov-11 Compiled by Mr. Lafferty Maths Dept.
Volume of a cuboid
S4
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Now try Ex 2
Ch8 (page 92)
30-Nov-11 Compiled by Mr. Lafferty Maths Dept.
S4 Starter Question
S4
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30-Nov-11 Compiled by Mr. Lafferty Maths Dept.
Liquid Volume
S4
Learning Intention Success Criteria
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1. To understand the 1. To know the term liquid
term liquid volume using volume.
millilitres and litres.
2. Work out volumes using
1ml and litres.
3. Answer to contain
appropriate units.
30-Nov-11 Compiled by Mr. Lafferty Maths Dept.
Liquid Volume
I’m a very
small
S4
How much water duck!
does this hold?
1 cm
1 cm
1 cm
Volume = l x b x h = 1 cm³
A cube with volume 1cm³ holds exact 1 millilitre of liquid.
A volume of 1000 ml = 1 litre.
30-Nov-11 Compiled by Mr. Lafferty Maths Dept.
Example 1
Liquid Volume
Working
S4 Volume = l x b x h
V = 6 x 3 x 12
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12 cm V = 216 cm³
Orange = 216 ml
Flavour
6 cm So the carton can hold
216 ml of orange juice.
Remember:
How much juice can
1 cm³ = 1 ml
this carton hold?
30-Nov-11 Compiled by Mr. Lafferty Maths Dept.
Example 2
Liquid Volume Working
S4 Volume = l x b x h
V = 100 x 30 x 50
V = 150 000 cm³
50 cm = 150 000 ml
= 150 litres
100 cm
How much water can So the fish tank can
3
1cm = 1 ml
this fish tank hold in 1000 litres of water.
hold 150ml = 1 litre
litres?
30-Nov-11 Compiled by Mr. Lafferty Maths Dept.
Liquid Volume
S4
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Now try Ex 3
Ch8 (page 94)
30-Nov-11 Compiled by Mr. Lafferty Maths Dept.
Starter Questions
Q1. Find the area of the triangle.
10cm
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Q2. Factorise 4x - 64
6cm
Q3. Calculate
40 - 1.65 50
Wednesday, 30 November 2011 Created by Mr.Lafferty 23
Volume of a Cylinder
Learning Intention Success Criteria
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1. To derive the formula for 1. To know formula.
the volume of a cylinder
and apply it to solve
problems. 2. Apply formula correctly.
3. Work backwards using
formula.
Volume of a Cylinder
The volume of a cylinder can be thought as being a pile
of circles laid on top of each other.
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Volume = Area x height h
= πr2 x h
Cylinder
= πr2h (circular Prism)
Volume of a Cylinder
Example : Find the volume of the cylinder below.
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5cm
V = πr2h 10cm
= π(5)2x10 Cylinder
= 250π cm (circular Prism)
Volume of Solids
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Now try Extension
Booklet
Starter Questions
Q1. 35% of 360
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Q2. Calculate 5 + 6 x 7
Q3. Expand 2( y – 5 )
Wednesday, 30 November 2011 Created by Mr.Lafferty 28
Volume of Solids
Prisms
Learning Intention Success Criteria
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1. To understand the 1. To know the volume
prism formula for formula for any prism.
calculating volume.
2. Work out volumes for
various prisms.
3. Answer to contain
appropriate units and
working.
Volume of Solids
Definition : A prism is a solid shape with
uniform cross-section
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Hexagonal Prism
Cylinder Triangular Prism
(circular Prism) Pentagonal Prism
Volume = Area of Cross section x length
Any Triangle Area
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h = vertical height
Sometimes
h called the
altitude
b
1
Area b h
2
Wednesday, 30 November 2011 Created by Mr.Lafferty 31
Any Triangle Area
Example 1 : Find the area of the triangle.
1
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Area b h
2
6cm
1
Area 8 6
2
8cm Area 24cm 2
Wednesday, 30 November 2011 Created by Mr.Lafferty 32
Volume of Solids
Definition : A prism is a solid shape with
uniform cross-section
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Q. Find the volume the triangular prism.
Triangular Prism
Volume = Area x length
3
= 20 x 10 = 200 cm 10cm 20cm
2
Volume of a
Triangular Prism
Working
1
Triangle Area = bh
2
2
= 2 x4 = 8 cm
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4cm Volume = Area x length
3
= 8 x 10 = 80cm
10cm
4cm
30-Nov-11 Created by Mr. Lafferty Maths Dept.
Example
Find the volume of the Working
triangular prism. 1
bh
Triangle Area = 2
2
= 3 x 3 = 9 cm
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Volume = Area x length
3
3cm = 9 x 30 = 270cm
30cm
6cm
Total Area
2
= 6+6+30+40+50 = 132cm
30-Nov-11 Compiled by Mr. Lafferty Maths Dept.
Volume of Solids
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Now try Extension
Booklet