These set the scene for each chapter, help with navigation through the coursebook and indicate the important concepts in each topic. Year 1 objectives are shown in bullet points whilst year 2 objectives are indicated with the chevron icon ( ) and highlighted in darker teal.
SAMPLE
INVESTIGATION/DISCUSSION
CAMBRIDGE O LEVEL MATHEMATICS: COURSEBOOK 2
This contains questions and activities on subject knowledge you will need before starting this chapter.
Exercises
At the end of some exercises you will find opportunities to help you assess your own work, or that of your classmates, and consider how you can improve the way you learn.
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These boxes contain questions and activities that will allow you to extend your learning by investigating a problem, or by discussing it with classmates. WORKED EXAMPLE
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MATHEMATICAL CONNECTIONS
SELF/PEER ASSESSMENT
LEARNING INTENTIONS
The key vocabulary appears in a box throughout each chapter and is highlighted in the text when it is first introduced. You will also find definitions of these words in the Glossary at the back of this book.
Throughout this book, you will notice lots of different features that will help your learning. These are explained below.
GETTING STARTED
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How to use this book
This feature will help you to link content in the chapter to what you have already learned, and highlights where you will use your understanding later in the course.
Appearing throughout the text, exercises give you a chance to check that you have understood the topic you have just read about and practise the mathematical skills you have learned. You can find the answers to these questions at the back of the Coursebook.
KEY WORDS
TIP The information in this feature will help you complete the exercises, and give you support in areas that you might find difficult.
FORMULA BOX
There is a summary of key points you should know so that you can check your progress at the end of each chapter.
SAMPLE
End-of-Chapter Review Exercise
A Brief History of This feature takes a look at the history of an important mathematician and mathematical concept to help you better understand new processes you are learning and how they came about. This icon tells you that you should complete an exercise without using your calculator.
REFLECTION
Cross-topic Review Exercise
The mid-chapter review exercise provides an opportunity for you to practise the mathematical skills you have learned so far throughout that chapter and check your understanding.
At the end of each chapter, you will find a set of mixed past-paper and authored practice questions. Completing these will help you to check your understanding of what you have learned throughout the chapter.
How to use this book These activities ask you to think about the approach that you take to your work, and how you might improve this in the future.
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SUMMARY
There will be two end-of-year cross-topic review exercises. One will be based on the content you have learned in year 1 and the other on the content you have learned in year 2. These questions will help you to check your understanding of the different mathematical skills you have learned throughout each year of your studies.
Mid-chapter Review
3
These contain important mathematical formulas you will need to learn and practise as you move though the course.
Chapter 3 Mensuration IN THIS CHAPTER YOU WILL: • solve problems involving perimeter and area of plane figures • calculate length of arc and the perimeter and area of sectors of circles calculate the area of segments of circles solve problems involving the surface area and volume of a cuboid, cylinder, prism, sphere, pyramid and cone solve problems involving the surface area and volume of a compound shape. Original material © Cambridge University Press & Assessment 2022. This material is not final and is subject to further changes prior to publication. We are working with Cambridge Assessment International Education towards endorsement of this resource. SAMPLE
• Area is measured in squared units. Calculating an area always involves the multiplication of two linear measurements.
• The perimeter (or circumference) and area of a circle and both involve the irrational number p • Flat, two-dimensional shapes are also called plane figures. Plane figures can be used to cover surfaces, but they cannot be used to fill up three-dimensional space. Check your skills 1 a 1 cm = 10 mm, so mm = 63 cm b 1 cm2 = mm2, so 32 mm2 = cm2 c 1 m2 = cm2, so 5200 cm2 = m2
areadiagonalperimeterlength
GETTING STARTED What do you already know?
Area and perimeter
The common units for lengths are millimetres (mm), centimetres (cm), metres (m) and kilometres (km).
TIP On plane figures with straight edges, there is no strict rule for what these two linear measurements are called. Some people andrectanglewouldheight,asdescribewoulda rectanglehaving widthandwhileotherssaythatthehaslengthbreadth.
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3.1
We usually refer to flat, two-dimensional shapes as plane figures. The size of a plane figure is calculated from two linear measurements. The general term that we use for all linear measurements is length, which includes all measurements of height, width, breadth, perimeter, radius, diameter, circumference, and even length itself.
SAMPLE
b Describe in words why plane figures cannot be used to fill up space.
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The perimeter of a plane figure is the total distance around the figure. We calculate the perimeter by adding together the lengths of all the sides.
3 Mensuration 5
2 The irrational number p is the ratio between two linear measurements. Which two linear measurements are these? 3 a Give the names of four flat, two-dimensional shapes whose areas can be found by multiplying their base length by their perpendicular height.
KEY WORDS
6 Plane figures with straight edges also have diagonals. A diagonal is a straight line that joins any two non-adjacent corners of a plane figure.
Figure 3.1: Areas of plane figures. Figure 3.2 shows you how to find the areas of two more plane figures: a rhombus and a kite. b a b a length, l Area = a × b21 Area = a × b21Area = l × h Rhombus Kite or height, h Figure 3.2: Area of a kite and a rhombus.
CAMBRIDGE O LEVEL MATHEMATICS: COURSEBOOK
Figure 3.1 reminds you how to find the areas of some plane figures that should already be familiar to you. Area is the amount of space that a figure takes up on a flat surface or plane. The units that we use for measuring area are mm2, cm2, m2, hectares (equal to 10 000 m2) and km2
It is important to note that the two lengths that you multiply together must be at right angles to each other. length, l base, b base, b base, b height, h height, h height, h b a length, l Rectangle Area = l × w Parallelogram Area = l × h height, h height, h width, w Trapezium Area = (a + b) × h21 Triangle Area = b × h21
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SAMPLE
3 Mensuration 7 A rhombus has two pairs of parallel sides and all four sides are the same length. A rhombus is a special type of parallelogram, so we can also use the length and perpendicular height of a rhombus to find its area – see the second diagram Thesein Figure 3.2.figures can be divided into four right-angled triangles by drawing their diagonals. b a b a length, l Area = a × b21 Area = a × b21Area = l × h Rhombus Kite or height, h If we draw a rectangle with area a × b around a rhombus or a kite, it is clear that the rhombus and the kite both occupy exactly half the area of the rectangle. Try this to convince yourself that the result is true. FORMULA BOX Area of rhombus or kite =× =×21 21ab product of diagonals WORKED EXAMPLE 1 a A parallelogram has an area of 297 cm2. Find its perpendicular height if the length of its base is 18 cm. b A triangle has an area of 75 cm2. Find the length of its base if its height is 7.5 cm. aAnswerlh h h ×= ×= == 297 18 297 16 529718 cm b 221 757575 75 20 1 75 2 bh b b ×= ×= == × cm Original material © Cambridge University Press & Assessment 2022. This material is not final and is subject to further changes prior to publication. We are working with Cambridge Assessment International Education towards endorsement of this resource. SAMPLE
CAMBRIDGE O LEVEL MATHEMATICS: COURSEBOOK 8 WORKED EXAMPLE 2 A right-angled triangle with side lengths x cm, (x + 4) cm and (x + 8) cm has a perimeter of 48 cm. Find the area of this triangle. Answer We sketch the triangle, knowing that the longest side, (x + 8) cm, is not used to calculate the area. x + 8 x + 4 x xx x x x ++++ = += = 48 48 3124812 The side lengths are 12 cm, 16 cm and 20 cm and the area is 21 161296×× = cm2 TIP The measurementstwo that we use to calculate area must be at right angles to each other. Exercise 3.1 In questions 1 to 12, find the area of each plane figure. 4.8 cm 1 cm3.5 3 cm12 13.1 cm 13cm 18.1 cm 2 7.4 cm cm5.5 20 cm 4 16 cm 0.4 cm 5 1 cm cm0.3 6 40 cm12 cm cmcm99 7 cm5.5 8.4 cm 6 cm4.5 cm 8 7.5 cm 9 58 cm cm60 61cm 12 cm 11 cm15.18.2 cm cm8.2 10 8.8 cm 5.6cm 10.2cmOriginal material © Cambridge University Press & Assessment 2022. This material is not final and is subject to further changes prior to publication. We are working with Cambridge Assessment International Education towards endorsement of this resource. SAMPLE
b A right-angled triangle has side lengths of 12 cm, 28.8 cm and 31.2 cm. Sketch the triangle and then calculate its area.
c Find the perimeter of a right-angled triangle whose shortest and longest sides are 10.8 cm and 18 cm long, and whose area is 77.76 cm2.
Group B: those that you can find the perimeter of, but would need to do extra calculations.
Group C: those that you cannot find the perimeter of. Put the diagram numbers into three groups, in discussion with your partner. Then find the perimeter of the figures in group A.
17 A right-angled triangle has an area of 56 cm2 and a perpendicular height of 8 cm. What is the length of its base?
The figures can be put into three groups:
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18 A rectangular field has an area of 0.24 hectares. Find the length of the field, given that its width is 25 metres.
Group A: those that you can find the perimeter of without doing any extra calculations.
ACTIVITY
13 Look again with a partner at the plane figures in questions 1 to 12
14 a A square has an area of 121 cm2. What is its perimeter?
15 A rectangle measures 84 cm by 200 cm. Find the area of the rectangle in metres squared.
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SAMPLE
3 Mensuration 9 cm5.5 8.4 cm 6 cm4.5 cm 7.5 cm 58 cm cm60 61cm 12 5 cm cm7 cm3 11 cm15.1 12.6 cm 8.2 cm cm8.2 10 8.8 cm 5.6cm 10.2cm DISCUSSION
19 The two parallel sides of a trapezium have lengths of 8 cm and 18 cm. The area of the trapezium is 130 cm2. How far apart are the two parallel sides?
16 The width of a rectangle is x cm less than its length. Given that the length of the rectangle is 15 cm, find a simplified expression, in x, for its: a perimeter b area.
The distance between the parallel sides is 16 cm, and the area of the parallelogram is 224 cm2 If the short parallel side is x cm long, show that 16x + 80 = 224 and find the length of the longer parallel side.
21 A rectangular sheet of card measures 20 cm by 35 cm. A triangle is to be removed from the card so that only 500 cm2 remains. Suggest the measurements of the triangle.
The width of the rectangle is 6 cm more than the width of the square. Find the total area of the two figures if the sum of their perimeters is 124 cm.
23 ABCD is a parallelogram in which AD = 10 cm and DC = 18 cm. A line drawn from D meets AB at X so that angle DXB = 90° and XB = 12 cm.
22 A square and a rectangle have equal lengths.
XA B D C 1218cmcm10 cm a Write down the distance from A to X b Given that DX : AX = 4 : 3, calculate the length of DX. c Find the area of: i triangle ADX ii trapezium BCDX.
24 A rectangular yellow card measuring 9 cm by 6 cm has 4 identical red rhombuses printed on it. The area of yellow card that can still be seen is 30 cm2 Suggest what the lengths of the two diagonals of the rhombus could be. Show your reasoning clearly.
10 20 a
The area of a trapezium is 93 cm2 Its parallel sides are 6 cm apart and one of the parallel sides is 11.6 cm long. How long is the other parallel side? b One parallel side of a different trapezium is 10 cm longer than the other.
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SAMPLE
CAMBRIDGE O LEVEL MATHEMATICS: COURSEBOOK
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The total surface area of a three-dimensional object is the sum of the areas of all of Drawingits faces. the faces of the object separately can be a useful aid to finding the areas of Forits surfaces.someobjects, such as cubes, cuboids and many prisms, the surfaces are all flat. A solid cube has six square faces; a solid cuboid has six rectangular faces, and a triangular prism has two triangular faces and three rectangular faces.
Now discuss what each individual piece of information could tell us about the figure in question 4.
CONNECTIONSMATHEMATICAL
C
E
F
The product of the diagonal lengths is 160 cm2. The perimeter is 80 cm.
SAMPLE
The perimeter of the figure is a multiple of 20 cm.
25
D
ACTIVITY With a partner, look again at the figure in question 4. We are not told whether it is a rhombus or not.
In the second part of this chapter, we will use the areas of plane figures to find the volume of a prism.
Invent some shapes, similar to those in the preceding exercise, for a partner to find the area and perimeter of. Discuss their answers. Were there some that were impossible to calculate because too little information was given? Swap roles.
Read the following pieces of information, A to G.
3.7 Surface area
Choose from ‘It is a rhombus’, ‘It is not a rhombus’ and ‘It may or may not be a rhombus.’
PEER ASSESSMENT
G The diagonals do not meet at right angles.
SUMMARY Are you able to …? find perimeters and areas of plane figures calculate lengths when given the areas of plane figures
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B
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KEY WORD surface area
3 Mensuration 11 DISCUSSION
The two diagonals are different lengths. The diagonals meet at right angles.
The product of the diagonal lengths is 320 cm2
A
WORKED EXAMPLE
12
Some of the surfaces of solid objects are curved. Solids with curved surfaces include cylinders, spheres, hemispheres and cones.
SAMPLE
A right pyramid has a rectangular base measuring 10 cm by 16 cm and a perpendicular height of 12 cm. Find the total area of its four triangular faces. Answer The pyramid has a rectangular base, so it has two pairs of identical triangular faces. 10 cm 13 cm 208 cm 16 cm10 cm Frontbackand Leftrightand 16 cm 12 cm Y X Y A X The height of the front and back triangles is AX AX is the hypotenuse of a right-angle triangle with short sides 102 5= and 12. AX =+ = 5121322 cm The height of the left and right triangles is AY AY is the hypotenuse of a right-angle triangle with short sides 162 8= and 12. AY =+ =812 20822 cm Total area of four triangular face s =× ()×+× ×2216132 1020882 208144222352=+ = cm2 The triangles at the front and back are not the same as the triangles at the left and right.
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TIP
Other objects, such as cylinders, spheres, hemispheres and cones, have surfaces that Theare curved.number of surfaces that these objects have depends on whether they are described as solid, closed, open or hollow.
CAMBRIDGE O LEVEL MATHEMATICS: COURSEBOOK
A A
Curved surfaces areas
14
3 Mensuration 13 Cylinder
The curved surface of a sphere can be covered by exactly four circles of the same radius.
The height (or length) of the rectangle is the same as the height (or length) of the cylinder, as shown in Figure 3.13.
Curved surface area of a sphere = 4pr2 , where r is the radius Hemisphere
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The shape of a cylinder’s curved surface is actually a rectangle. The width of the rectangle is equal to the circumference of the circular end of the cylinder, 2pr
FORMULA BOX
OPENCUT OPEN 2πr h
Curved surface area of a cylinder = 2prh, where r is the radius of the circular cross-section and h is the height Sphere
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SAMPLE
The curved surface of a hemisphere can be covered by exactly two circles of the same radius.
FORMULA BOX
FORMULA BOX
Curved surface area of a hemisphere = 2pr2, where r is the radius Cone
The shape of a cone’s curved surface is actually a sector of a circle. The radius of the sector is equal to the slant height of the cone, l. The arc length of the sector is equal to the circumference of the base of the cone, 2pr, as shown in Figure 3.14.
Figure 3.13: Curved surface of a cylinder.
SAMPLE
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Curved surface area of a cone = prl, where r is the radius of the circular base and l is the slant height.
Figure 3.14: Curved surface of a cone.
WORKED EXAMPLE 15 Find the total surface area of a closed cylinder of radius 2 cm and length 10 cm. Give the answer in terms of p and also to 3 significant figures. Answer
The cylinder has two flat faces that are both circles of radius 2 cm. The curved surface is a rectangle. The height of this rectangle is 10 cm and the width is equal to the circumference of the circular ends, which is 2pr The diagram shows the cylinder and its three surfaces drawn separately. 2 cm 2 cm 10 cm 10 cm 2πr 2 cm Total surface area = ++ × + =× ×+ ×× = pp p pp pp rr r rr 2222 210 22220 20 2 = 484 2 p or 151 cm
FORMULA BOX
CAMBRIDGE O LEVEL MATHEMATICS: COURSEBOOK 14 CUT OPEN h l l l r 2πr
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Calculate the total curved surface area of the object.
SAMPLE
Give the answer in terms of p and also correct to 1 decimal place. Answer For the hemisphere r = 6 cm
For the cone r = 6 cm and the height, h = 14 − 6 = 8 cm. Curved surface area of hemisphere 62 = 21 4 2272 2 2 × = =× × = p p p p r r oro cm226194 2 . ...
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The slant height is the hypotenuse of a right-angled triangle with short sides of r = 6 cm and h = 8 cm. l =+ =86 1001022 = cm Curved surface area of cone 610or c = = = p p p rl ×× 60188495 mm2 In terms of p, the total curved surface area is 7260 cmpp p+= 132 2
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The diagram shows a solid object that consists of a solid cone sitting on top of a solid hemisphere. The width of the object is 12 cm and the height of the object is 14 cm. 12 cm 14 cm
WORKED EXAMPLE 16
To find the curved surface area of the cone, we need to work out the slant height, l
3 Mensuration 15
Find the total surface area of:
A cube has a total surface area of 486 cm2. Find the volume of the cube.
Find, in terms of p, the surface area of a sphere that has diameter 8 cm.
3.7
1
3
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A solid cylinder has radius 4 cm and length 15 cm. Find in terms of p: a the total area of the two circular ends b the area of the cylinder’s curved surface c the total surface area of the cylinder in terms of p.
2
7
10
9
A cube has a volume of 405.224 cm3. Calculate the total area of the cube’s six faces.
Find, in terms of p, the curved surface area of a cone that has radius 3 cm and height 4 cm.
a a cube of side 5 cm b a cuboid that measures 1 cm by 2 cm by 3 cm c a cuboid that measures 10 cm by 15 cm by 20 cm.
5
Exercise16
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In questions where a diagram is not provided, you are advised to make your own sketch.
6 Find the radius of a sphere that has a surface area of 100 cm2
8
11
CAMBRIDGE O LEVEL MATHEMATICS: COURSEBOOK
A solid wooden cone has a diameter of 18 cm and a height of 18 cm. Find: a the slant height of the cone b the area of the cone’s curved surface c the total area of the cone’s two surfaces.
4
A solid cylinder has a length of 15 cm and a volume of 540p cm3. Find: a the radius of the cylinder b the area of the cylinder’s curved surface in terms of p c the total area of the cylinder’s three surfaces in terms of p
SAMPLE
The cross-section of a triangular prism is a right-angled triangle with sides of lengths 8 cm, 15 cm and 17 cm. The length of the prism is 20 cm. a Find the area of the prism’s cross-section. b Calculate the total area of the prism’s five faces.
A right pyramid has a square base of side 12 cm and a perpendicular height of 8 Calculatecm. the total surface area of the pyramid’s four triangular faces.
d The cone is made from material with a density of 1.6 g/cm3, and the cylindrical base is made from material with a density of 1.8 g/cm3 Find, in kilograms correct to 3 significant figures, the mass of the object.
c Calculate the cost of silver-plating the whole object at a cost of $0.75 per square centimetre.
13 The solid object shown is made from a solid cylinder of diameter 16 cm fixed to a solid cone of the same diameter. The height of the whole object is 22 cm and the height of the cylinder is 8 cm. 16 cm 22 cm 8 cm a Calculate, correct to 1 decimal place, the total area of the object’s two curved surfaces.
3 Mensuration
17 12 A tin of paint covers an area of 50 m2 and costs $15. Calculate the cost of painting the curved surface of a hemispherical dome of radius 14 metres.
b Find, to the nearest whole number, the total surface area of the object.
b Calculate the area of the exterior surface of the cone that is unpainted.
SAMPLE
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14 The exterior surface of an inverted cone of radius 21 cm and perpendicular height 72 cm is painted to a height of 48 cm. 21 cm 72 cm 48 cm a Show that the slant height of the painted surface of the cone is exactly 50 cm.
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c Calculate the size of the sector angle θ. d Find, in terms of p, the curved surface area of the cone. e Calculate, correct to 1 decimal place, the volume of the cone.
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a Show that each cone has a radius of 10 cm.
18 15 A circle of radius 40 cm is cut from a large sheet of paper. The circle is then cut into four equal-sized sectors. Each sector is then made into a hollow cone by joining the straight edges together.
b Find, in terms of p, the curved surface area of each cone.
SAMPLE
17 A right cone, Q, has a curved surface area of 100 cm2 State the curved surface area of a similar right cone that has twice the radius and twice the perpendicular height of Q. 18 The diagram shows an open container filled to a height of 10 cm with liquid polish.Thetopsection of the container is a frustum of height 3 cm, which is attached to a cylinder whose hollow base is a hemisphere of diameter 8 cm. The diameter of the open top of the frustum is 2 cm and the total height of the container is 20 cm. 10 cm 3 cm 2 cm 20 cm 8 cm
16 The sector shown can be made into a right cone of base radius 5 cm. 18 cmθ a The perpendicular height of the cone is p cm Find the value of p. b Find, in terms of p, the arc length of the sector.
CAMBRIDGE O LEVEL MATHEMATICS: COURSEBOOK
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19 a Show that the small cone that has been removed to make the frustum has a height of 1 cm. b Calculate the capacity of the open container, giving your answer in millilitres in terms of p. c
SAMPLE
3 Mensuration
d Find the percentage of the space inside the container that is filled with liquid polish. e
The cross-sections of the troughs are: a right-angled isosceles triangle, a semi-circle, an isosceles trapezium and a rectangle. All the troughs are 90 cm wide, 45 cm deep and 2 metres long. They are constructed from the same thickness of steel. The economy rating of a trough is a measure of ‘capacity per unit area of steel used’. Find the economy rating of each style of trough. Rank them in order, starting with the most economical.
Briefly explain, without doing any calculations, how you know that the container is less than half filled with liquid polish.
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The thin metal that makes up the container costs $4.65 per square metre. Calculate the total cost of the thin metal required to make 144 identical containers.
INVESTIGATION
19 Work on this investigation with a partner. A farmer wants to buy a steel trough for watering her animals. There are four styles of trough to choose from: A, B, C and D Each style has a different cross-section. 90 cm 90 cm 90 cm 90 cm 45 cm 45 cmA B C D
ACTIVITY
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REFLECTION In some of the problems you have worked through in the previous exercise, you need multiple steps to reach the final answer. Think about the accuracy of each of the answers along the way, before you reach the final answer. How can you make sure that the final answer is as accurate as it needs to be?
20 We have already looked at how the measurements on sectors and right cones are connected. We know that Pythagoras’ theorem can be used to find lengths of the parts of a right cone. We also know that the surface of a cone is a sector of radius l and arc length 2pr CUTh l l l r 2πr θ Discuss with a partner some of the other things that you know about sectors and right cones. Together, investigate how the size of the sector angle, θ, can be expressed in terms of just two of the three lengths r, h and l.
SUMMARY Are you able to …? see the benefit of drawing the surfaces of three-dimensional objects separately to help work out the surface understandareathat cylinders, cones, spheres and hemispheres have curved surfaces use the formulae for calculating surface areas of prisms, spheres, hemispheres, pyramids and cones
CAMBRIDGE O LEVEL MATHEMATICS: COURSEBOOK 20DISCUSSION
SAMPLE
1 litre of paint covers 2 square metres. Calculate the amount of paint used.
[Cambridge O level Mathematics (4024), Paper 2 Q5, November 2020]
[Cambridge O level Mathematics (4024), Paper 11 Q19, November 2013]
1 B A G H D E C F 2.10 1.85 1.55 2.25 The diagram shows a garden shed positioned on horizontal ground. It is in the shape of a prism with trapezium ABCD as its cross-section.
End-of-chapter review exercise
b The roof of the shed, CGHD, is painted.
2 Volume of a cone = 13 2 p rh Cone 1 has radius 2x cm and height 7x cm. Cone 2 has radius x cm and height 4x cm. Find an expression, in terms of p and x, for the difference in the volume of the two cones. Give your answer in its simplest form.
c Calculate the angle of elevation of D from F
3 Mensuration 21
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The base of the shed, ABFE, is a rectangle.
AB = 1.55 m, AD = 2.25 m, BC = 1.85 m and BF = 2.10 m. a Calculate the volume of the shed.
SAMPLE
The cylinder has radius 15 cm and height 42 cm. The curved surface area of the cone and the cylinder are equal. Find the value of y [Cambridge O level Mathematics (4024), Paper 11 Q24, June 2020]
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The cone has radius 28 cm and slant height y cm.
SAMPLE
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4 Curved surface area of a cone = prl
O is the centre of circles with radii 1 cm, 2 cm, 3 cm, 4 cm and 5 cm.
i Calculate the total area of the shaded sections, giving your answer in terms of p. ii Calculate the fraction of the total area of the cover that is metal (unshaded). Give your answer in its simplest form. [Cambridge O level Mathematics (4024), Paper 11 Q19, June 2013]
The diagram shows the metal cover for a circular drain. Water drains out through the shaded sections.
22
B C D A O
The cover has rotational symmetry of order 6 and BÔC = 40°. a Calculate the area of the shaded section ABCD, giving your answer in terms of p b The total area of the metal (unshaded) sections of the cover is 553 2 p cm .
CAMBRIDGE O LEVEL MATHEMATICS: COURSEBOOK 3
The diagram shows a cone and a cylinder. y 28 42 15
i Calculate the value of h.
The company sells the chocolate bars to shops for $0.70 each bar.
A company makes and packages chocolate bars.
ii A shop buys one carton of chocolate bars.
Each carton is a cuboid with internal dimensions 30 cm by 28 cm by h cm. 80 boxes fill one carton exactly.
c
• They sell 3 5 of the bars at a profit of 30%.
• They sell each of the remaining bars at $0.84. Calculate the overall percentage profit made by the shop from selling all 80 bars. [Cambridge O level Mathematics (4024), Paper 21 Q5, June 2020]
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i The company makes 40% profit on each bar it sells. Work out the cost to the company of producing each bar.
SAMPLE
3 Mensuration 23 5
7.5 cm 14 cm 6 cm x cm This box contains a chocolate bar. The box is in the shape of a triangular prism.
ii One day, the company packs 37 500 of these boxes into cartons. How many complete cartons are packed that day?
a Show that x = 4.5 b These boxes are packed into cartons.
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