Sha Tin College Mathematics Department Key Stage 4 Extended Level Course
Formulae
Need to Know
Area rectangle = w x l
Area triangle = ½ bh
Area parallelogram = bh
Area trapezium = ½ h (a + b)
Area circle = πr 2
Circumference circle = 2πr= πd

Arc length = x πd
Sector Area =
360 o

360 o x πr 2
Surface Area of Cuboid =
2(lw + lh + wh)
Volume of Cuboid = l x w x h
Volume of Cylinder = π r 2 h
Volume of any prism =
Area of cross- section x height
Volume of Cone =
1
3
π r
2 h
Volume of Pyramid =
1 base area x height
3
1 hectare (ha) = 100m x 100m = 10 000m
2
Given
Total Surface Area of Cylinder = 2 πr
2
+ 2
πrh
Curved Surface Area of Cone = πrl
Surface Area of Sphere =
4πr 2
Volume of Sphere =
4
3
πr 3
Sha Tin College Mathematics Department KS 4 ASSIGNMENT Mensuration 1

#1 Arrange in ascending order of size
3.22 m 3
2
9 m 32.4 cm.
Answer < < [2]
#2 Three students are asked to estimate the area of a desk top.
Their answers are
0.4 m
2
3500 cm
2
and
5
12
m
2
.
(a) Place these estimates in order, beginning with the smallest.
Answer (a) , , [2]
(b) If the true area is 0.41 m 2 , which of these estimates is the most accurate?
Answer (b) [1]
#3 A rectangular field has dimensions 450m by 300m. What is its area in hectares?
[1]
#4 Change 1.2 cubic metres to cubic centimetres.
........................................ cubic centimetres
(Total 2 marks)
Total for Section A /8
Sha Tin College Mathematics Department KS 4 ASSIGNMENT Mensuration 2

#1 A school hall is to have its interior walls and ceiling painted.
The hall is a cuboid with length 30 m, width 20 m and height 4 m.
Windows and doors, of total surface area 200 m 2 , are not to be painted. NOT TO SCALE
(a) Calculate the total surface area to be painted. m 2 [2] Answer (a)
(b) One litre of paint covers 18 m
2
. It is sold in 5 litre tins.
How many tins of paint are needed to complete the task?
Answer (b) tins [2]
#2
= 1 cm 2
(a) Find the area of the shape.
…...………. cm 2
(1)
(b) Find the perimeter of the shape.
…...…………… cm
(2)
Sha Tin College Mathematics Department KS 4 ASSIGNMENT Mensuration 3

#3
Diagram NOT drawn accurately
42 m
140 m
20 m
120 m
The diagram shows a car park.
Mrs Roberts is selling the car park. She will accept any offer that is more than £28 per square metre.
Mr Patel offers £194 700 for the car park..
Will Mrs Roberts accept Mr Patel’s offer for the car park?
You must show how you reached your decision.
Decision ………………….
(6 )
Total for Section B /13
Sha Tin College Mathematics Department KS 4 ASSIGNMENT Mensuration 4

#1 (a) (i) Calculate the circumference of a bicycle wheel of diameter 0.64 m.
Answer (a)(i) m [2]
(ii) Calculate the number of complete turns the wheel makes when the bicycle travels 700 m.
Answer (a)(ii) [2]
#2
54 cm Diagram NOT accurately drawn
10 cm
The diagram shows a solid cylinder.
The radius of the cylinder is 54 cm.
The height of the cylinder is 10 cm.
Calculate the curved surface area of the cylinder.
Give your answer correct to three significant figures.
……………….
(3)
Sha Tin College Mathematics Department KS 4 ASSIGNMENT Mensuration 5

#3.
A can of drink is in the shape of a cylinder.
The can has a radius of 4 cm and a height of 15 cm.
Diagram NOT accurately drawn
15 cm
#4
4 cm
Calculate the volume of the cylinder.
Give your answer correct to 3 significant figures.
…………………….. [2]
40°
O
Diagram NOT accurately drawn
9 cm
The diagram shows a sector of a circle, centre O .The radius of the circle is 9 cm.
The angle at the centre of the circle is 40°.
(a) Find the perimeter of the sector.
Leave your answer in terms of
π
.
…………………….. [2]
(b) Find the area of the sector to 3 significant figures
...........................cm
[2]
Total for Section C /13
Sha Tin College Mathematics Department KS 4 ASSIGNMENT Mensuration 6

#1
The diagram shows a trench which has been dug out of level ground so that a cylindrical water pipe can be laid.
NOT TO SCALE
The cross-section, ABCD , of the trench is a trapezium with horizontal sides of length 1.1 m and 0.8 m and height 0.7 m. The length of the trench is 500 m.
(a) Calculate the volume of earth removed. [3]
(b) If 1 m
3
of earth has a mass of 1.8 tonnes, calculate the mass of earth removed. [2]
(c) The diameter of the pipe is 0.5 m. After the pipe has been laid earth is replaced until the ground is again level.
Calculate the percentage of the earth which is not replaced.
[4]
Sha Tin College Mathematics Department KS 4 ASSIGNMENT Mensuration 7

(d) If water flows through the pipe at 0.8 m/s, how many litres will flow through the pipe in 1 hour? [1 m
3
= 1000 litres.]
[3]
#2 What volume of stone would be needed to construct a solid, square-based pyramid with length of base 45 m and perpendicular height of 20m?
…………………………. [2]
The length of a sloping edge was found to be 25m.
What area of stone would be covered if the outer surfaces of the pyramid were painted?
…………………………. [4]
Sha Tin College Mathematics Department KS 4 ASSIGNMENT Mensuration 8

#3
Diagram NOT accurately drawn
6 cm
8 cm
The diagram shows a solid wooden cone.
The height of the cone is 6 cm.
The base radius of the cone is 8 cm.
(a) Find the volume of the cone.
Give your answer as a multiple of

.
………………… cm 3
(2)
Total for Section D /20
Sha Tin College Mathematics Department KS 4 ASSIGNMENT Mensuration 9

Main Learning Objectives
RECAP (A) Be familiar with the metric units of measurement and be able to convert between units. i.e. mm, cm, m, km; mm
2
, cm
2
, m
2
, ha, km
2
; mm
3
, cm
3
, ml, cl, l, m
3
; g, kg, t
Theory of Knowledge – applying mathematical knowledge to solving a real life problem.
RECAP (A) Find the perimeter and area of rectangles.
RECAP Find the perimeter and area of rectangles, triangles and compound shapes derived from these. Know the formulae.
RECAP Find the perimeter and area of parallelograms and trapeziums Know the formulae.
Investigating – making drawings, being systematic, looking for patterns, using a table, generalizing.
RECAP Find the circumference and area of a circle. Know the formulae.
NEW Find arc length and area of sector. Know the formulae. Apply to finding the perimeter of a sector.
NEW Find the surface area of a cuboid and a cylinder. Know the formulae for cuboid only. Formula for curved surface area of cylinder will be given.
NEW Find the surface area of a sphere, cone, and a pyramid. Know the formulae for pyramid only. Formula for curved surface area of sphere and cone will be given.
RECAP Find the volume of a cuboid, a cylinder and other common prisms. Know the formula for cuboid, the volume of a cylinder will be given.
NEW Find the volume of a sphere, cone, and a pyramid. Formula for volume of all these objects will be given.
Investigating/Modelling, drawing a picture, trial and improvement, listing outcomes, generalizing.
NEW/RECAP Find areas and volumes of compound shapes.
Investigating – drawing a picture, looking for relationships, generalizing.
Investigating/Modelling, drawing a picture, trial and improvement, listing outcomes, generalizing.
Sha Tin College Mathematics Department KS 4 ASSIGNMENT Mensuration 10