A brilliant for YR 10 and YR 11 GCSE students studying volume and surface area in class also very good for revising when coming up to assessments or mock examinations.

1. Volume and surface area

2. Lo-to be able to understand the different
formula’s for volume and surface area
Lo- to apply this to work out Questions
given

3. Starter: find the area of these shapes
1) 2) 3)
4)
15cm2 50cm2
24cm2
45cm2

4. What do you think the formula’s are for these shapes?
Length x width x
depth/heightLength x width x
depth/height
X R2 X perpendicular
height 3

5. Sphere Cube Cuboid Cone Cylinder
Square based
pyramid
Triangular
based pyramid
Triangular
prism
Hexagonal
prism
Sphere
Cube
Cuboid
Cone
Cylinder
Square based
pyramid
Triangular
based pyramid
Triangular
prism
Hexagonal
prism
How many 3D shapes can you name?
1 2 3 4 5
6 7 8 9

6. REVISION NOTES

7. Volume is measured in cm3

8. How to work out
the volume of a
shape.
Each shape has a
different formula
here are a few…
You have 1 min
to copy this.

9. Surface area is measured in
cm2

10. How to work out
surface area of a
shape .
Each shape has a
different formula
here are a few..
You have 1min
to copy this

11. EXAMPLE
HAVE A GO FIRST BEFORE I SHOW YOU THE
ANSWER

12. 1. (a) Christopher buys a fish tank.
The dimensions of the tank are 91 cm by
32 cm by 35 cm.
(i) Calculate the volume of the tank in cm³.
...................................................................
...................................................................
...................................................................
...................................
(ii)How many litres of water will the tank hold
when full?
(1000 cm³ = 1 litre)
...................................................................
...................................................................
(2)
35cm
32cm
91cm
(i) Volume of a cuboid = l x b x h
V = 91 x 32 x 35
V = 101920 cm³
(ii) 101920 ÷ 1000 = 101.92 litres

13. Work!
TRY AND WORK OUT THESE

14. Q1
Try to work
out this
Question you
have 1mins. Work out the total surface area of the cube.
(3)

15. Q2
Try to work
out this
Question you
have 1mins.
Work out the total surface area of the triangular
prism.
(4)

16. Q3
Try to work
out this
Question you
have 1 mins.
Work out the volume of the prism.
(3)

17. Q4
Try to work
out this
Question you
have 1mins.
Work out the volume of the eraser. Give the units of your
answer
(3)

18. Q5
Try to work
out this
Question you
have 1 mins.
Work out the volume of the prism.
_ _ _ _ _ cm3
(3)

19. Q6
Try to work
out this
Question you
have 1mins. Work out the volume of liquid needed to fill the glass.
________ cm3
(3)

20. Q7
Try to work
out this
Question you
have 1 mins.
12 cm
10 cm
Diagram NOT accurately drawn
The diagram represents a cone.
The height of the cone is 12 cm.
The diameter of the base of the cone is 10 cm.
Calculate the curved surface area of the cone.
Give your answer as a multiple of .
…………….. cm2
(3)

21. Challenge questions – Find the Volume
V = 48cm3 V = 50cm3 V = 108cm3
 Try to work
out these
Questions
you have
2mins.

22. Now try these exam style
Questions.

23. A cylinder has a radius of 5 cm.
(a) Calculate the circumference of a
circular end of the cylinder.
[2 marks]
The cylinder has a volume of 250 cm3.
(b)Calculate the height of the cylinder.
[3 marks]

24. A school hall is in the shape of a
cuboid.
The school hall is 30 m long, 12 m
wide and 4 m tall, as shown in the
diagram.
(a) Calculate the volume of the hall.
[2 marks]
(b) Calculate the total area of the
four walls of the hall.
[3 marks]

25. The diagram shows a cylinder.
The diameter of the cylinder is 10 cm.
The height of the cylinder is 10 cm.
(a) Calculate the volume of the
cylinder.
Give your answer in terms of π.
[3 marks]

26. The diagram, shows a container in the
shape of a cuboid.
(a) Work out the volume of the
container. State the units of your
answer.
[3 marks]
Ben wants to paint the four outside walls
and the top of the container.
One tin of paint covers 6 m2.
(b) How many tins of paint does Ben
need?
You must show all your working.
[4 marks]

27. The diagram shows a cylinder.
The diameter of the cylinder is
20 cm.
The height of the cylinder is 2
cm.
Work out the volume of the
cylinder.
Use π = 3.14
[3 marks]

28. Two spheres of radius 5 cm
just fit inside a tube.
Calculate the volume inside
the tube not filled by the
spheres.
[5 marks]

29. EXTENSION

30. 3𝑐𝑚
10𝑐𝑚
Volume = 𝟗𝟎𝝅 = 𝟐𝟖𝟐. 𝟕𝟒𝒄𝒎 𝟑
Surface Area = 𝟕𝟖𝝅 = 𝟐𝟒𝟓. 𝟎𝟒𝒄𝒎 𝟐
?
?

32. challenge extension task
𝑟 = 𝟏. 𝟏𝟑𝒎ℎ = 𝟒. 𝟖𝟒𝒎 𝑟 = 𝟐. 𝟖𝟖𝒎 𝑟 = 𝟐. 𝟖𝟐𝒎
𝒙
𝟐𝒙𝟏𝟎𝒄𝒎
𝒙
𝒙
𝑉 = 720𝑐𝑚35 6
𝑆𝐴 = 27𝜋
𝒙
7 𝑆𝐴 = 75𝜋
𝑥 = 𝟑𝑥 = 𝟔 𝟔 = 𝟏𝟒. 𝟕𝒄𝒎
𝑥 = 𝟓