1. Volumes by Counting Cubes
Volume is the amount of space a 3D - shape takes up
1cm
1cm
1cm
One Unit of Volume is the “CUBIC CENTIMETRE”
= 1 centimetre cube
= 1 cm³

2. Volumes by Counting Cubes
This shape is made up of 1 centimetre cubes placed next to each other. What is its volume in cm³?
1cm
1cm
1cm
1cm
= 2 centimetre cubes
= 2 cm³

3. Volumes by Counting Cubes
This shape is made up of 1 centimetre cubes placed next to each other. What is its volume in cm³
1cm
1cm
1cm
= 3 centimetre cubes
= 3 cm³

4. Volumes by Counting Cubes
One unit of Volume is the “CUBIC CENTIMETRE”
3cm
2cm
4cm
Volume = 24 centimetre cube
= 24 cm³

5. A short cut ! Volume = 6 x 3 x 4 = 72 cm³ Volume = length x breadth
height
Area of rectangle
breadth
length
Volume = 6
x 3
x 4
= 72 cm³
Volume =
length
x breadth
x height

6. Example 1 27cm 5 cm 18 cm Working Volume = l x b x h V = 18 x 5 x 27
Heilander’s
Porridge Oats
V = 18 x 5 x 27
V = cm³
27cm
5 cm
18 cm

7. Example 2
Working
Volume = l x b x h
V = 2 x 2 x 2
V = 8 cm³
2cm

8. Liquid Volume Volume = l x b x h = 1 cm³
I’m a very small duck!
How much water 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.

9. Example 1 Working Volume = l x b x h V = 6 x 3 x 12 V = 216 cm³
Liquid Volume
Working
Orange
Flavour
Volume = l x b x h
V = 6 x 3 x 12
12 cm
V = 216 cm³
= 216 ml
3 cm
6 cm
So the carton can hold
216 ml of orange juice.
How much juice can
this carton hold?
Remember:
1 cm³ = 1 ml

10. Example 2 Working Volume = l x b x h V = 100 x 30 x 50 V = 150 000 cm³
Liquid Volume
Working
Volume = l x b x h
V = 100 x 30 x 50
V = cm³
50 cm
= ml
= 150 litres
30 cm
100 cm
How much water can this fish tank hold in litres?
1cm3 = 1 ml
1000 ml = 1 litre
So the fish tank can hold 150 litres of water.

11. Revision of Area
The Square
The Rectangle
The RAT b h l b l l

12. Face Edges and Vertices
Don’t forget the faces edges and corners we can’t see at the back
Face Edges and Vertices
The shape below is called a cuboid.
It is made up of FACES, EDGES and VERTICES.
Edges are where the two faces meet (lines)
Faces are the
sides of a shape
(surface area)
Vertices where lines meet (corners)

13. Face Edges and Vertices
Calculate the number of faces edges and vertices for a cuboid.
Face Edges and Vertices
6 faces
12 edges
Front and back are the same
8 vertices
Top and bottom are the same
Right and left are the same

14. Face Edges and Vertices
Calculate the number of faces edges and vertices for a cube.
Face Edges and Vertices
6 faces
12 edges
Faces are squares
8 vertices

15. Face Edges and Vertices
Calculate the number of faces, edges and vertices for these shapes
Face Edges and Vertices
5 faces
9 edges
6 Vertices
2 faces
1 edges
1 Vertices
Cone
Triangular
Prism
Cylinder
Sphere
3 faces
2 edges
1 faces
0 Vertices
0 edges
0 Vertices

16. Surface Area of the Cuboid
What is meant by the term surface area?
The complete area of a 3D shape

17. Find the surface area of the cuboid
Example
Find the surface area of the cuboid
Working
Front Area = l x b
= 5 x 4 =20cm2
Top Area = l x b
= 5 x 3 =15cm2
4cm
Side Area = l x b
= 3 x 4 =12cm2
3cm
5cm
Total Area =
= 94cm2
Front and back are the same
Top and bottom are the same
Right and left are the same

18. Find the surface area of the cuboid
Example
Find the surface area of the cuboid
Working
Front Area = l x b
= 8 x 6 =48cm2
Top Area = l x b
= 8 x 5 =40cm2
6cm
Side Area = l x b
= 6 x 5 =30cm2
5cm
8cm
Total Area =
= 236cm2
Front and back are the same
Top and bottom are the same
Right and left are the same

19. Volume of Solids Definition : A prism is a solid shape with
uniform cross-section
Hexagonal Prism
Cylinder
(circular Prism)
Triangular Prism
Pentagonal Prism
Volume = Area of Face x length

20. Sometimes called the altitude
Any Triangle Area
h = vertical height
Sometimes called the altitude h b 20

21. Any Triangle Area Example 1 : Find the area of the triangle. 6cm
Area = 24cm²

22. Volume of Solids Definition : A prism is a solid shape with
uniform cross-section
Q. Find the volume the triangular prism.
Triangular Prism
Volume = Area of face x length
= 20 x 10 = 200 cm3
10cm
20cm2

23. Volume of a Triangular Prism
Working
Triangle Area =
= 2 x4 = 8 cm2
4cm
Volume = Area x length
= 8 x 10 = 80cm3
10cm
4cm
Find the volume of the triangular prism

24. Find the volume of the triangular prism.
Example
Find the volume of the triangular prism.
Working
Triangle Area =
= 3 x 3 = 9 cm2
Volume = Area x length
= 9 x 30 = 270cm3
6cm
3cm
30cm
Total Area
= = 132cm2

25. Find the surface area of the right angle prism
Example
Find the surface area of the right angle prism
Working
Triangle Area =
= 2 x3 =6cm2
Rectangle 1 Area = l x b
= 3 x10 =30cm2
4cm
5cm
Rectangle 2 Area = l x b
3cm
10cm
= 4 x 10 =40cm2
Rectangle 3 Area = l x b
2 triangles the same
= 5 x 10 =50cm2
1 rectangle 3cm by 10cm
Total Area
= = 132cm2
1 rectangle 4cm by 10cm
1 rectangle 5cm by 10cm

26. Surface Areaof a Triangular Prism
Working
Triangle Area =
= 2 x4 = 8 cm2
5cm
Rectangle 1 Area = l x b
4cm
= 5 x10 =50cm2
10cm
Rectangle 2 Area = l x b
4cm
= 5 x10 =50cm2
2 triangles the same
Rectangle 3 Area = l x b
2 rectangle the same 5cm by 10cm
= 4 x 10 =40cm2
1 rectangle 4cm by 10cm
Total Area
= = 156cm2

27. Volume of a Cylinder Volume = Area x height = πr2 = πr2h h x h
The volume of a cylinder can be thought as being a pile
of circles laid on top of each other.
Volume = Area x height h
= πr2
x h
Cylinder
(circular Prism)
= πr2h

28. Volume of a Cylinder V = πr2h = π(5)2x10 = 250π cm
Example : Find the volume of the cylinder below.
5cm
Cylinder
(circular Prism)
10cm
V = πr2h
= π(5)2x10
= 250π cm

29. Surface Area of a Cylinder 2πr h Total Surface Area = 2πr2 + 2πrh
The surface area of a cylinder is made up of 2 basic shapes can you name them.
Cylinder
(circular Prism)
2πr
Curved Area =2πrh
Top Area =πr2
Roll out
curve side  h
Bottom Area =πr2
2 x Circles
Rectangle
Total Surface Area = 2πr2 + 2πrh

30. Surface Area of a Cylinder = (2 x π x 3²) + (2 x π x 3 x 10)
Example : Find the surface area of the cylinder below:
3cm
Surface Area = 2πr2 + 2πrh
10cm
= (2 x π x 3²) + (2 x π x 3 x 10)
= 2 x π x x π x 30
Cylinder
(circular Prism)
= cm²

31. Surface Area of a Cylinder = 2 x π x 3 x 9 = 169.64 cm2
Radius = 1diameter 2
Example : A net of a cylinder is given below.
Find the curved surface area only!
6cm
Curved Surface Area = 2πrh
= 2 x π x 3 x 9
9cm
= cm2