1. Volume & Surface Area of Solids www.mathsrevision.com Revision of Area
Revision of Volume and Surface Area
Volume of a Prism
Volume of a Cylinder
Volume of a Pyramid
Curved Area of a Cylinder
Volume of a Sphere
Exam Type Questions

2. Starter Questions a2 – 3b2 = 57 Q1. True or false
Q2. Write down the probability of picking out a number
greater than 20 in the national lottery.
Q3. If a = -3 and b = -4 does
a2 – 3b2 = 57
Q4. Calculate
Tuesday, 11 April 2017
Created by Mr.Lafferty

3. Revision of Areas www.mathsrevision.com Any Type of Triangle
Level 4
Any Type of Triangle
Rhombus and kite
Parallelogram
Trapezium
Circle

4. Compiled by Mr. Lafferty Maths Dept.
Area
Level 4
Learning Intention
Success Criteria
We are revising area of basic shapes.
Know formulae.
Use formulae correctly.
Show working and
appropriate units.
11-Apr-17
Compiled by Mr. Lafferty Maths Dept.

5. Area Example : Find the area of the V – shape kite.
Level 4
Example : Find the area of the V – shape kite.
4cm
7cm
Tuesday, 11 April 2017
Created by Mr.Lafferty

6. Composite Areas We can use our knowledge of the basic areas
Level 4
We can use our knowledge of the basic areas
to work out more complicated shapes.
Example : Find the area of the arrow.
5cm
3cm
6cm
4cm
Tuesday, 11 April 2017
Created by Mr.Lafferty

7. Composite Areas 8cm www.mathsrevision.com 11cm 10cm
Level 4
Example : Find the area of the shaded area.
8cm
11cm
4cm
10cm
Tuesday, 11 April 2017
Created by Mr.Lafferty

8. Created by Mr. Lafferty Maths Dept.
Composite Areas
The Circle
Level 4
Example : Find the area of the shape
Area = rectangle + semicircle
20cm
5 cm
11-Apr-17
Created by Mr. Lafferty Maths Dept.

9. Area Now try TJ 4+ Ex 16.1 Ch16 (page 121) www.mathsrevision.com
Level 4
Now try TJ 4+
Ex 16.1
Ch16 (page 121)
Tuesday, 11 April 2017
Created by Mr.

10. Q4. Rearrange into the form y =
Starter Questions
Q1. Find the area of the triangle.
10cm
3cm
4cm
Q2. Expand out and simplify 2w2 – 3(2w – 5)
Q3. True or false
Q4. Rearrange into the form y =
2y – 3x + 7 = 0
Tuesday, 11 April 2017
Created by Mr.Lafferty

11. Compiled by Mr. Lafferty Maths Dept.
Volume & Surface Area
Level 4
Learning Intention
Success Criteria
We are revising volume and surface area of a cuboid.
Know formulae.
Use formulae correctly.
Show working and
appropriate units.
11-Apr-17
Compiled by Mr. Lafferty Maths Dept.

12. Compiled by Mr. Lafferty Maths Dept.
Volume of a cuboid
3cm
4cm
6cm
Level 4
18 cubes fit the base.
= 1 centimetre cube = 1 cm³
4 layers of 18 cubes
= 4 x 18
= 72 centimetre cubes
= 72 cm³
11-Apr-17
Compiled by Mr. Lafferty Maths Dept.

13. Compiled by Mr. Lafferty Maths Dept.
A short cut !
3cm
4cm
6cm
Level 4
height
Area of rectangle
breadth
length
Volume = 6
x 3
x 4
= 72 cm³
Volume =
length
x breadth
x height
11-Apr-17
Compiled by Mr. Lafferty Maths Dept.

14. Compiled by Mr. Lafferty Maths Dept.
Example
Working
Volume = l x b x h
Level 4
Heilander’s
Porridge Oats
V = 18 x 5 x 27
V = cm³
27cm
5 cm
18 cm
11-Apr-17
Compiled by Mr. Lafferty Maths Dept.

15. Compiled by Mr. Lafferty Maths Dept.
Example
Working
Volume = l x b x h
Level 4
V = 2 x 2 x 2
V = 8 cm³
2cm
11-Apr-17
Compiled by Mr. Lafferty Maths Dept.

16. Compiled by Mr. Lafferty Maths Dept.
Example
Find the volume of the composite shape.
Level 4
VT = V1 + V2
7 cm
3 cm
5 cm
VT =
10 cm
9 cm
8 cm
VT = 825 cm3
V1 = l x b x h
= 3 x 5 x 7
V2 = l x b x h
= 105 cm³
= 8 x 10 x 9
= 720 cm³
11-Apr-17
Compiled by Mr. Lafferty Maths Dept.

17. Find the length the cuboid
Example
Find the length the cuboid
This just an equation.
We know how to solve them !
Level 4
4 cm
Volume = L x B x H
V=200cm3
200 = L x 5 x 4
5 cm
200 = 20L
10 cm L
20L = 200
L = 10
11-Apr-17
Compiled by Mr. Lafferty Maths Dept.

18. Compiled by Mr. Lafferty Maths Dept.
Example
Liquid Volume
Working
Volume = l x b x h
Level 4
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-Apr-17
Compiled by Mr. Lafferty Maths Dept.

19. Face Edges and Vertices
Don’t forget the faces edges and corners we can’t see at the back
Face Edges and Vertices
Level 4
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)
11-Apr-17
Compiled by Mr. Lafferty Maths Dept.

20. Face Edges and Vertices
Calculate the number of faces edges and vertices for a cuboid.
Face Edges and Vertices
Level 4
6 faces
12 edges
Front and back are the same
8 vertices
Top and bottom are the same
Right and left are the same
11-Apr-17
Compiled by Mr. Lafferty Maths Dept.

21. Face Edges and Vertices
Calculate the number of faces edges and vertices for a cube.
Face Edges and Vertices
Level 4
6 faces
12 edges
Faces are squares
8 vertices
11-Apr-17
Compiled by Mr. Lafferty Maths Dept.

22. Find the surface area of the cuboid
Example
Find the surface area of the cuboid
Working
Level 4
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
11-Apr-17
Compiled by Mr. Lafferty Maths Dept.

23. Now try TJ 4+ Ex 16.2 Ch16 (page 122) Volume & Surface Area
Level 4
Now try TJ 4+
Ex 16.2
Ch16 (page 122)
Tuesday, 11 April 2017
Created by Mr.

24. Starter Questions Q1. True or false 2(x – 6) - 2(x + 6) = 0
Q2. Does x 20 = Explain your answer
Q3. Factorise 2y2 + 3y +2
Q4. Calculate
Tuesday, 11 April 2017
Created by Mr.Lafferty

25. Volume of Prisms www.mathsrevision.com Learning Intention
Level 4
Learning Intention
Success Criteria
We are learning how to calculating volume of any
prism given area.
1. Calculate the volume for
various prisms.
2. Solution must include
appropriate units and working.

26. Volume of Prisms www.mathsrevision.com
Level 4
Definition : A prism is a solid shape with
uniform cross-section
Hexagonal Prism
Cylinder
(circular Prism)
Triangular Prism
Pentagonal Prism
Volume = Area of Cross section x length

27. Volume of Prisms www.mathsrevision.com
Level 4
Definition : A prism is a solid shape with
uniform cross-section
Hexagonal Prism
Cylinder
(circular Prism)
Triangular Prism
Pentagonal Prism
Volume = Area of Cross section x length

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

29. Volume of Prisms Now try TJ 4+ Ex 16.3 Ch16 (page 124)
Level 4
Now try TJ 4+
Ex 16.3
Ch16 (page 124)
Tuesday, 11 April 2017
Created by Mr.

30. Starter Questions Q1. Find the area of the parallelogram Q2. Factorise7 7
Q2. Factorise
4x + 40
Q3. A can of beans is reduce by 15% to 25p.
Find the price before the reduction.
Q4. The speed of light is metres per sec.
True or false in scientific notation 3 x 108.
Tuesday, 11 April 2017
Created by Mr.Lafferty

31. Volume of a Cylinder www.mathsrevision.com Learning Intention
Level 4
Learning Intention
Success Criteria
We are learning how to derive the formula for the volume of a cylinder and apply it to solve problems.
To know formula.
Apply formula correctly.
Work backwards using formula.

32. Volume of a Cylinder Volume = Area x height = πr2 = πr2h
Level 4
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

33. Volume of a Cylinder V = πr2h = π(5)2x10 = 250π cm3 = 784.5 cm3
Example : Find the volume of the cylinder below.
5cm
Cylinder
(circular Prism)
10cm
V = πr2h
= π(5)2x10
= 250π cm3
= cm3

34. Volume of a Cylinder Now try TJ 4+ Ex 16.4 Ch16 (page 125)
Level 4
Now try TJ 4+
Ex 16.4
Ch16 (page 125)
Tuesday, 11 April 2017
Created by Mr.

35. Starter Questions -(a2) + b2 = 5 Q1. Factorise
Q2. Write down the probability of picking out a number
less than 30 in the national lottery.
Q3. True or false if a = -1 and b = -2
-(a2) + b2 = 5
Q4. Explain why
Tuesday, 11 April 2017
Created by Mr.Lafferty

36. Volume of a Pyramid www.mathsrevision.com Learning Intention
Level 4
Learning Intention
Success Criteria
We are learning how to use the formula for the volume of ANY pyramid and apply it to solve problems.
To know formula.
Apply formula correctly.
Work backwards using formula.

37. Volume of a Pyramid www.mathsrevision.com
Level 4
cone
The volume of any pyramid can be
calculated using the formula
A = Area of base
h = height

38. Volume of Pyramid www.mathsrevision.com
Level 4
Q. Find the volume the pyramid.
12m
100m2

39. Volume of a Cone www.mathsrevision.com h r
Level 4 h r
If the above cone has radius 15cm and height
of 10 cm. Calculate it’s volume.

40. Volume of a Pyramid Now try TJ 4+ Ex 16.5 Ch16 (page 127)
Level 4
Now try TJ 4+
Ex 16.5
Ch16 (page 127)
Tuesday, 11 April 2017
Created by Mr.

41. Starter Questions Q1. Expand out and simplify 3(x – 2) - ( - 3x + 4)
Q2. Factorise 2x2 – 16x
Q3. True or false
Q4. By rearranging in y = , find the gradient and where
the straight line crosses the x-axis y + 4x - 3 = 0
Tuesday, 11 April 2017
Created by Mr.Lafferty

42. Surface Area of a Cylinder www.mathsrevision.com Learning Intention
Level 4
Learning Intention
Success Criteria
We are learning how to calculate the surface area of a cylinder by using basic areas.
To know how to split up a cylinder.
2. Calculate the surface area of a cylinder.

43. Surface Area of a Cylinder 2πr h Total Surface Area = 2πr2 + 2πrh
Level 4
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
Total Surface Area = 2πr2 + 2πrh

44. Surface Area of a Cylinder = 2π(3)2 + 2π x 3 x 10 = 18π + 60π
Level 4
Example : Find the surface area of the cylinder below:
3cm
Surface Area = 2πr2 + 2πrh
10cm
= 2π(3)2 + 2π x 3 x 10
= 18π + 60π
Cylinder
(circular Prism)
= 245 cm2

45. Surface Area of a Cylinder D = 25 25 D = π www.mathsrevision.com
Diameter = 2r
Example : A net of a cylinder is given below.
Find the diameter of the tin and the total
surface area.
D = 25 25 π
9cm
25cm
D =
= 7.96 cm
Surface Area = 2πr2 + 2πrh
= 2π(3.98) 2 + 2π(3.98)x9
= = cm2

46. Now try TJ 4+ Ex 16.6 Ch16 (page 129) Surface Area of a Cylinder
Level 4
Now try TJ 4+
Ex 16.6
Ch16 (page 129)
Tuesday, 11 April 2017
Created by Mr.

47. Starter Questions Q1. Find the area of the triangle. 10cm
Q2. Factorise 4x2 – 64x
6cm
Q3. Calculate
Q4. Rearrange equation in y =
y – 2x + 5 = 0
Tuesday, 11 April 2017
Created by Mr.Lafferty

48. Volume of Solids www.mathsrevision.com Learning Intention
Level 4
Learning Intention
Success Criteria
We are learning how to use the sphere formula and use it to solve real-life problems.
To know the volume formula for a sphere.
Work out volumes for spheres.
Answer to contain
appropriate units and working.

49. Volume of a Sphere www.mathsrevision.com D = diameter r
Level 4
D = diameter r D
Q. If the above sphere has radius 10cm.
Calculate it’s volume.

50. Volume of a sphere Q. Find the volume the composite shape.
Level 4
Q. Find the volume the composite shape.
Volume = Cylinder + half a sphere
½ sphere
Cylinder r 2m
h = 6m

51. Now try TJ 4+ Ex 16.7 Ch16 (page 130) Volume of a sphere
Level 4
Now try TJ 4+
Ex 16.7
Ch16 (page 130)
Tuesday, 11 April 2017
Created by Mr.

58. Part b on next slide