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CSEC Mathematics Section 4 – Measurement

Pythagoras’ Theorem (Page 462, R. Toolsie’s Textbook)

Pythagoras’ theorem states that in any right-angled triangle, the square on the hypotenuse (the longest side which is opposite to the right angle) is equal to the sum of the squares on the two other sides.

Exercise

Answer the following.

1. In a triangle ABC, angle C = 900, a = 5 cm and

b = 12 cm. Find c. Answer 13 cm

A

B C

Hypotenuse (AC = b) c

a b

AC2 = AB2 + BC2

or b2 = c2 + a2.

b =

AB = or c = .

(2)

2. In a triangle PQR, angle Q = 900, p = 8 cm and

r = 15 cm. Find q. Answer 17cm

3. In a triangle XYZ, X = 900, y = 3 cm and

x = 5 cm. Find z. Answer 4 cm

4. In a triangle LMN, M = 900, m = 25 cm and

n = 24 cm. Find l. Answer 7cm

5. Find the length of the unknown side.

Answer:

a. 10.82m b. 9.75cm c. 8.31 mm d. 5.39 m

6. A ladder 6.5 m tall is placed against a wall.

Calculate the horizontal distance from the foot of

the ladder to the base of the wall, given that the

a. b. c. d.

6 m

9 m

12 cm 7 cm

9.8 mm 5.2 mm

(3)

Ans: 5.66 m

7. A light post is 10 feet tall. A man is standing

6 feet away from the light post. How far is the

foot of the man from the top of the light post?

Ans: h = 11.66 feet

Average Speed (Page 156, R. Toolsie’s Textbook)

The speed of a body is defined as its rate of change of distance with time.

Average Speed (s) = .

Some units of average speed are:

kmh– 1 or km/h – kilometre per hour,

ms-1 or m/s – metres per second.

(4)

Time taken (t) =

Exercise

Answer the following.

1. A bullet takes 3 seconds to travel a distance of 1200 m. Calculate the average speed of the bullet.

Answer 400 m/s or 400 ms-1

2. A car is travelling at a constant speed 54 km/h.

MAY 2015 – Question 5a

a. Calculate the distance it travels in hours.

Answer 121.5 km

b. Calculate the time, in seconds, it takes to travel

315 metres, given that 1 km/h = m/s.

(5)

of time between the two readings, calculate the:

a. distance travelled in kilometres

Answer 126 km

b. average speed of the aircraft in km/h.

Answer 630 km/h

MAY 2009 – Question 4a

4. John left Port A at 0730 hours and travels to Port B in the same time zone.

a. He arrives at Port B at 1420 hours. How long did

the journey take? Answer 6hrs 50 mins

b. John travelled 410 kilometres. Calculate his – 1

Time Distance Travelled (km)

08:55 am 09:07 am

(6)

Answer 60 km/h

JANUARY 2008 – Question 4a

5. How long will it take to travel 96 km at an

average speed of 24 km/h? Answer 4 hrs

6. The following is an extract from a bus

schedule. The bus begins its journey at Belleview, travels to Chagville and ends its journey at St. Andrews. JANUARY 2012 Question 4a

Town Arrive Depart Belleview _____ 6:40 a.m.

Chagville 7:35 a.m. 7:45 a.m.

St.

Andrews

8:00 a.m. ______

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c. How long did the bus take to travel from Belleview to Chagville?

d. The bus travelled at an average speed of 54 km/hour from Belleview to Chagville.

Calculate, in kilometres, the distance from Belleview

to Chagville. Answer 49.5 km

Converting from one Square Unit to Another (Page 107, R. Toolsie’s Textbook)

Some square units of length in ascending order are: mm2, cm2, dm2, m2, dam2, hm2, km2

When converting from a larger square unit to a smaller square unit, we multiply by the respective power of ten ‘squared’. For example,

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When converting from a smaller square unit to a

larger square unit, we divide by the respective power of ten ‘squared’. For example,

i. 305 hm2 = 305 102 km2 = 3.05 km2

ii. 600 mm2 = 600 10002 m2 = 0.0006 m2

Exercise

Write the correct value on the line to make the statement true.

1. 704.35 cm2 = _______ m2 Ans: 0.070435 m2

2. 904.75 km2 = ______ dam2 Ans: 9,047,500 dam2

3. 5012 mm2 = ______ cm2 Ans:50.12 cm2

4. 0.0256 km2 = ______ m2 Ans:25600 m2

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It is impossible to draw the actual size of the map of a country, house or car on a sheet of paper. Hence, we use a scale in order to draw a representation of these shapes on paper. The scale is given as the ratio of a length on a map to the actual distance on the

ground. A scale of 1 : 5,000,000 means 1 cm

measured on the map is equal to 5,000,000 cm or 50 km measured on the ground.

Note: The ratio of a length on the model or map to

the actual length is 1: n

The ratio of an area on the model or map to the

actual area is 1: n2

The ratio of a volume on the model or map to the

actual volume is 1: n3.

(10)

When changing from the actual distance to the map distance we divide.

To change from km to cm multiply by 100,000

To change from cm to km divide by 100,000

Exercise

Answer the following.

1. The scale on a road map is 1: 25,000.

a. What is the actual distance, in metres, between two villages represented by 3.5 cm on the map?

Answer:Actual distance 875 m

b. What is the actual area, in metres, of a playing field represented on the map by a rectangle 0.5 cm long and 0.3 cm wide?

(11)

2. The scale on a map is 1:20,000. The actual

distance between two points is 3.8 km. Calculate the number of centimetres that should be used to

represent this distance on the map.

Answer: Map distance = 19 cm

3. Write the following scales in the form 1: x.

a. 1 millimetre = 1 metre Answer 1:1000

b. 2 cm = 6 m Answer 1:300

c. The map shown below is drawn on a grid of 1 cm squares. P, Q, R and S are four tracking stations. The

scale of the map is 1:2000.

(12)

i. Determine, in centimetres, the distance from Q to R on the map.

ii. Determine, by counting, the area in square centimetres of the plane PQRS on the map.

iii. Calculate the actual distance, in kilometres,

between Q and R. Answer 0.12 km

iv. Calculate the actual area, in square metres, of the

plane PQRS. Answer 7,200 m2

4. The diagram below shows a map of an island

Q

P R

S

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drawn to a scale of 1 : 50,000.

MAY 2014 – Question 4

a. Copy and complete each of the following sentences:

i. 1 cm on the map represents ___________ cm on the island.

ii. An area of 1 cm2 on the map represents an area of

_________ cm2 on the island

iii. Given that 1 km = 100,000 cm, a distance of 1 cm on the map represents a distance of

_________ km on the island.

Forest Reserve

L

(14)

b i. L and M are two tracking stations. State, in centimetres, the distance LM on the map.

ii. Calculate the actual distance, in kilometres, from

L to M on the island. Answer 4 km

c i. The area shaded on the map is a forest reserve.

By counting squares estimate, in cm2, the area of the

forest reserve as shown on the map.

ii. Calculate, in km2, the actual area of the forest

reserve. Answer: 6.75 km2

5. The diagram below shows a map of a playing field drawn on a grid of 1 cm squares. The scale of the

map is 1 : 1,250. JANUARY 2010 – Question

(15)

a. Measure and state, in centimetres, the distance

from S to F on the map. Answer SF = 7.81 cm

b. Calculate the distance, in metres, from S to F on

the actual playing field. Answer 97.625 m

c. Daniel ran the distance from S to F in 9.72 seconds. Calculate his average speed, giving

your answer correct to 3 significant figures, in:

i. m/s ii. km/h

Answer 10.0 m/s , 36.2 km/h

S

(16)

6. The map shown below is drawn to a scale of 1:

50,000. MAY 2009 – Question 4b

a. Measure and state, in centimetres, the distance on

the map from L to M along a straight line.

Answer 7 cm

b. Calculate the actual distance, in kilometres, from

L to M. Answer 3.5 km

c. The actual distance between two points is 4.5 km. Calculate the number of centimetres that

should be used to represent this distance on the map.

Answer 9 cm

L

M ●

(17)

7. The diagram below shows a map of a golf course drawn on a grid of 1 cm squares. The scale of the map is 1: 4000.

MAY 2007 – Question 4a

Using the map of the golf course, find the:

a. distance, to the nearest m, from the South Gate to

East Gate. Answer Map Distance = 0.03 m

Actual distance = 120 m

b. distance, to the nearest m, from the North Gate to

the South Gate. Answer Map distance = 0.058 m

Actual distance = 232 m

● East Gate ●

(18)

c. area on the ground represented by 1 cm2 on the

map. Answer 40002 cm2 = 16,000,000 cm2

d. actual area of the golf course, giving your answer in square metres.

Answer 26 × 1600 m2 = 41,600 m2

8. The distance between two places on a map is 200,000 cm and the actual distance on the

ground is 8,000 km. Determine the scale of the map.

Answer 1 : 4000

9. Find the scale used on a map, given that the distance between two schools on the map is

(19)

Polygon

A polygon is a plane closed figure bounded by

straight lines. A regular polygon is a polygon which has all its sides equal in length and its interior angles are all equal in size. For example, a square or an

equilateral triangle.

NB All squares are rectangles but not all rectangles are squares.

Types of Polygons (Page 479, R. Toolsie’s Textbook)

Name of Polygon

Number of Sides

Sum of its Interior Angles

Sum of the

exterior angles

Triangle 3 1 1800 = 3600

(20)

1800

Quadrilateral 4 2 1800 =

3600 360

0

Pentagon 5 3 1800 =

5400

3600

Hexagon 6 4 1800 =

7200 360

0

Heptagon 7 5 1800 =

9000

3600

Octagon 8 6 1800 =

10800

3600

Nonagon 9 7 1800 =

12600

3600

Decagon 10 8 1800 =

14400

3600

Undecagon 11 9 1800 =

16200

3600

Dodecagon 12 10 1800 =

18000

(21)

The sum of the interior angles of a polygon is:

S = (n – 2) 1800 or (2n – 4) 900 where n is the

number of sides of the polygon.

The sum of the exterior angle of any polygon is 3600.

The number of sides of a polygon is the same as the number of angles.

The interior angle + the exterior angle of any polygon = 1800.

The size of each interior angle of a regular polygon =

.

Exercise

Answer the following.

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a. 8 sides Answer 10800

b. 4 sides Answer 3600

c. 12 sides Answer 18000

d. 19 sides Answer 30600

e. 36 sides Answer 61200

2. Find the number of sides of a regular polygon with an exterior angle measuring:

a. 300 Answer 12 sides b. 900 Answer 4 sides c. 1200 Answer 3 sides

d. 450 Answer 8 sides

(23)

c) 1500 Ans: 12 sides d) 1650 Ans: 24 sides e) 1720 Ans: 45 sides

f) 1440 Ans: 10 sides g) 1740 Ans: 60 sides

4. What is the size of each interior angle of a regular:

a) octagon Ans: 1350

b) quadrilateral Ans: 900

c) 18 sided polygon Ans: 1600

d) icosagon Ans: 1620

e) 16 sided polygon Ans: 157.50

f) 30 sided polygon Ans: 1680

g) nonagon Ans: 1400

(24)

A triangle is a three sided plane shape (or figure) bounded by three straight lines.

Two triangles are said to be congruent if they are the

same. That is, they have all corresponding sides equal in length and the corresponding angles are all equal in size.

An isosceles triangle has two sides equal in length and two angles equal in size.

An equilateral triangle is a triangle with all sides equal in length and all interior angles equal in size.

The sum of the three interior angles of any given

b b

m

a a

(25)

If any side of a triangle is produced, (i.e. extended) then the exterior angle formed is equal to the sum of the two interior opposite angles.

Ext. Angle = The sum of the two Int. Opp. Angles. That is, c = a + b

Exercise

Find the size of the angle marked by a letter.

a. b.

Answer w = 1100 Answer b = 620

y = 450

650

700 w y b 560 Ext. Angle Interior Opposite Angle

Int. Adj. Angle

e a

b

(26)

c. d.

Answer h = 680 Answer h = 470

p = 440 d = 1330

Similar Triangles (Page 458, R. Toolsie’s Textbook)

Angle A = Angle X = 240; Angle B = Angle Y =

630 and C = Z = 930

AB = 8 cm; YX = 12 cm; BC = 5 cm; YZ = 7.5 cm and AC = 6 cm; XZ = 9 cm

X Z Y A B C 8 cm 6 cm

5 cm 7.5 cm

(27)

corresponding sides are the same. The length of a side of one triangle is k times the corresponding length of the side of the other triangle, where k is a

constant called the scale factor. That is,

> 1

The area of one triangle is k2 times the area of the

other triangle. That is,

the area of triangle XYZ = k2 the area of triangle

ABC. Hence,

Note: If k < 1, then the

If k > 1, then the

Exercise

(28)

1. ABC is similar to PQR such that A= P, B= Q and C = R. Find the length of:

i. AC ii. BC

Answer: i. AC = 15 cm ii. BC = 13.333 cm

2. The triangles DEG and LMN are similar. Calculate the length of:

i. MN ii. DG

Answer: i. MN = 12 cm ii. DG = 6 cm

M

L N

E

D G

8 cm

4 cm 6 cm 12 cm

A

B C

P

Q R

10 cm

(29)

3. Two similar triangles, OPQ and RST are such that

the ratio of their sides is . If the area of the smaller

triangle, OPQ is 16 square units, calculate the area of

the larger triangle RST. Answer = 100 square units

4. Two similar triangles, WXY and JKL are such that the ratio of their sides is 3. If the area of the

smaller triangle, JKL is 45 square units, calculate the area of the larger triangle WXY.

Answer = 405 sq. units

5. Two similar triangles, BCD and TUV are such

that the ratio of their sides is . If the area of the

larger triangle, TUV is 64 square units, calculate the area of the smaller triangle BCD.

(30)

The perimeter of a plane closed shape is the total length of the boundaries/sides of the shape.

The perimeter of a circle is the circumference (C) of the circle. That is, C = 2 r, where is the value

or 3.142 (3 dec. pl.) and r is the radius of the

circle.

Radius of a circle (r) =

Note: The diameter of a circle = 2 radius.

The radius of a circle =

The arc of a circle is any part of the circumference of

arc radius

(31)

The sector of a circle is the region bounded by two radii and an arc.

The segment of a circle is the region bounded by a chord and an arc.

The chord is a line touching two points on the circumference of the circle.

AREA

Area is a measure of the surface covered or the region covered. Area is measured in square units e.g. cm2, mm2, m2, km2 or dm2.

The Area of a Triangle can be calculated as follows:

The area of a triangle, A = ,

(32)

(altitude) of the triangle. The base and the height of a

triangle are always at right angle (900) to each other.

The base of a triangle,

Height (h) =

The area of a triangle where the base or height cannot be identified and three sides of the triangle is given:

where s is the

.

The area of a triangle, given two sides and the angle

between them is: Area =

Area of a Rectangle

The area (A) of a rectangle is the length times the

a b

(33)

Note: All squares are rectangles but not all rectangles are squares.

Area of a Square

The area of a square = Length Length or width

width or length width . That is, Area = L2 or W2.

Length of a square (L) =

Exercise

Answer the following.

1. The diagram below shows an isosceles triangle CDE. G is the mid-point of CD.

MAY 2013 Question 4a

a. Measure and state, in centimetres, the length of DE. Answer DE = 5 cm

E

D C

(34)

b. Measure and state, in degrees, the size of ECD.

Answer ECD = 360

c. Determine the perimeter of the triangle CDE,

given that GE = 3 cm. Answer 18 cm

d. Calculate the area of the triangle CDE.

Answer = 12 cm2

2. In the diagram below, not drawn to scale, AEC and ADB are straight lines.

ABC = ADE = 900. AC = 10 m, AB = 8 m

and DB = 3.2 m.

MAY 2013 Ques. 3b

a. Calculate the length of BC. Answer BC = 6 m

b. Explain why triangles ABC and ADE are similar.

10 m 10 m

8 m C

B A

E

(35)

Answer The shape is the same and the

corresponding interior angles are the same.

c. Determine the length of DE.Answer DE = 3.6 m

d. Calculate the area of the trapezium BCED.

Ans: 15.36 m2

3. The diagram below, not drawn to scale, shows a

wooden toy in the shape of a prism, with cross

section ABCDE. F is the midpoint of EC and BAE

= CBA = 90°. Calculate the:

MAY 2010 Question 3b

a. length of EF. Answer EF = 3 cm

b. length of DF. Answer DF = 4 cm

c. area of the face ABCDE. Answer Area = 42 cm2

D

A

D B

5 cm

5 cm 6 cm

E

C

(36)

4. In the triangle PQR, calculate the length of:

i. RQ ii. PT iii. QP

Ans. i. RQ = 14.7 m ii. PT = 10.1 m iii. QP = 10.98 m

5.

a. Calculate the length of AB. Answer AB = 10 cm

b. Determine the length of CD. Ans.CD = 17.5 cm

c. Find the length of CA. Answer CA = 19.5 cm

d. Compute the area of ABDC.

P

R Q

T 14.5 m

10.4 m 4.3 m

O B

D C

26 cm

(37)

The area of a circle is Area = radius (r) radius (r) = r2

The area of a semi-circle = radius (r) radius (r)

= r2

Radius of a circle (r) =

Area of a Sector

The area of a sector is = radius (r) radius (r) =

r2 , where is the sector angle.

Length of an arc

The length of an arc, L = 2 r =2 r

Area of a Trapezium

(38)

Exercise

Answer the following.

Calculate the area of the trapezium below.

Answer Area = 80 cm2

Area of a Rhombus

A rhombus is a parallelogram with all its sides equal in length.

NOTE: The base is always at right angle (900) to the

height.

(39)

Note: Opposite sides of a rectangle, rhombus or parallelogram are equal.

Exercise

Answer the following.

1. a) Use the rhombus below to state the length of the side:

i. AB ii. BD Answer i. AB = 19 cm

ii. BD = 19cm iii EB = 11.7 cm

b. Calculate the area of the rhombus above.

Answer Area 285 cm2

(40)

Exercise

Answer the following.

a) Calculate the area of the parallelogram below.

Ans. Area = 143 sq. units

b) Find the length of QR. Ans. QR = 13.15 units

Q P

S

(41)

1. Find the area of the shaded region.

a. b.

Answer a. 36 cm2 b. mm2

2. The diagram below, not drawn to scale, shows a circle with centre O and a square OPQR.

The radius of the circle is 3.5 cm. Calculate the area of the:

a. circle Answer 38.5 cm2

b. square OPQR. Ans. 12.25 cm2

c. shaded region. Answer 2.625 cm2

JANUARY 2008 Question 4b

8 mm

13 mm

3.5 cm

O P

R Q

5 cm 9 cm

(42)

3a. Find the area of a square with length 6 mm.

Answer Area = 36 mm2

b. What is the length of a square with area 81 m2?

Answer length = 9 m

4a. A piece of wire is bent to form a square of area

121 cm2. Calculate the:

i. length of each side of the square. Answer 11 cm

MAY 2011 Question 4b

ii. perimeter of the square. Answer 44 cm

b. The same piece of wire is bent to form a circle.

Use to calculate the:

(43)

a) area of the sector AOB. Answer 21.21 cm2

b) length of the arc AB. Answer 9.43 cm

c) perimeter of the sector AOB. Answer 18.43 cm

6. The diagram below, not drawn to scale, shows the

sector of a circle with centre O. MON = 450 and

ON = 15 cm. Use . Calculate, giving your

answer correct to 2 decimal places the:

JANUARY 2007 Question 7b

a. length of the minor arc MN

Answer MN = 11.78 cm

b. perimeter of the figure MON Ans. P = 41.78 cm

c. area of the figure MON Ans. Area = 88.31 cm2

M

O N

(44)

12 m 9 m 15 m 5 m 5 cm 14 cm 3 cm 8 cm 4 cm b. a.

7. Calculate the perimeter and the area of the following shapes.

Answer: Perimeter a. 54 m b. 50 cm Area a. 90 m2 b. 82 cm2

8. The diagram below, not drawn to scale, represents the plan of a floor. The broken line RS, divides the floor into two rectangles, A and B.

MAY 2008 Question 5

a. Calculate the length of RS.

Answer RS = 6 m

(45)

Answer P = 40 m

d. Calculate the area of the entire floor.

Answer RS = 74 m2

e. Section A of the floor is to be covered with

flooring boards measuring 2 m by 20 cm. How many flooring boards are needed for covering Section A?

Answer 125 flooring boards

Solids (Page 136, R. Toolsie’s Textbook)

(46)

The cross-section is the face or shape which a solid possesses throughout its entire length.

Volume of a Solid

Volume is the amount of space occupied by an object or solid. It is measured in cubic units such as cubic

centimetre (cm3), cubic metre (m3), cubic millimetre

(mm3) or cubic kilometre (km3). It can also measured

in litres.

Note: 1 litre = 1000 cm3

A Cuboid

rectangular cross-section circular cross-section length

Fig. 1 - Cuboid

(47)

The volume of a cuboid = length width height

= L W H

Length = Width =

Height =

A cuboid has 6 rectangular faces. The total surface area is the sum of the area of each of the six faces.

Note: All cubes are cuboids, but not all cuboids are cubes.

A Cylinder

A closed cylinder has three faces. It has two flat circular faces and one curved face. I has two edges.

The volume of a cylinder (V) = or

height

(48)

Height (h) = where = or 3.142.

The total surface area of a cylinder = curved surface

area + the two flat surface area = 2 + 2 .

A Triangular Prism or Triangle Based Prism (Wedge)

The Volume of a triangular prism = area of the cross-section of the prism length of the prism

= area of the triangle face length of the prism

cross-sections

(49)

sum of the area of the two triangle faces + sum of the area of the three rectangular faces.

Exercise

Answer the following.

1. A cylinder is 0.14 m high with a diameter of

40 cm. What is the volume of the cylinder in:

a) cm3 ? b) m3 ?

Ans. a) 17,600 cm3 b) 0.0176 m3

2. The diagram below, not drawn to scale, shows two cylindrical water tanks, A and B. Tank B

has a diameter of 8 m and height 5 m. Both tanks are filled with water. Take = 3.14.

(50)

a. Calculate the volume of water in tank B.

Answer Volume = 251.2 m3

b. If the area of the base of A is 314 m2, calculate the

length of the radius of tank A. Answer r = 10 m

c. Tank A holds 8 times as much water than tank B.

Calculate the height, h of tank A. Answer h = 6.4 m

3. For each triangular prism below, calculate the:

a. volume of the prism.

Answer Volume i. 144 cm3 ii. 66 cm3

(51)

i.

ii.

4. The diagram below, not drawn to scale, shows the cross-section of a prism in the shape of a sector of a circle, with centre O and radius 3.5 cm. The angle at

the centre is 2700. Use .

MAY 2012 Question 4

a. Calculate the:

B

A

C O 3.5 cm

(52)

ii. perimeter of the sector OABC. Ans. P = 23.5 cm

iii. area of the sector OABC.

Answer: Area = 28.875 cm2

b. The prism is 20 cm long and is a solid made of tin. Calculate the:

i. volume of the prism. Answer: Vol. = 577.5 cm3

ii. mass of the prism, to the nearest kg, given that

1 cm3 of tin has a mass of 7.3 kg.

Answer: Mass = 4,215.75 kg

5. The diagram below, not drawn to scale, shows a prism of length 30 cm. The cross-section WXYZ is a

(53)

a. volume, in cm3, of the prism

Answer: Volume = 4,320 cm3

b. total surface area, in cm2, of the prism.

Answer: TSA = 1,728 cm2

6. The diagram below, not drawn to scale, shows a

prism of volume 960 cm3. The cross-section ABCD

is a square. The length of the prism is 15 cm.

Calculate the: MAY 2007 Question 4b

a. length of the edge AB, in cm. Ans. AB = 8 cm

b. total surface area of the prism, in cm2.

Ans. TSA = 608 cm2

7. A company makes cereal boxes in the shape of a right prism. Each large box has dimensions 25 cm by

Y

X W Z 30 cm

C

(54)

a. Calculate the volume in cubic centimetres of one

large cereal box. Answer: Vol. = 7,200 cm3

b. Calculate the total surface area of one large cereal

box. Answer TSA = 2,776 cm2

c. The cereal from one large box can exactly fill six small boxes, each of equal volume.

i. Calculate the volume of one small cereal box.

Answer: Vol. = 1200 cm3

ii. If the height of a small box is 20 cm, list two different pairs of values which the company can use for the length and the width of a small box.

Answer l × w = 60 cm2

36 cm

25 cm

(55)

1 cm × 60 cm or 2 cm × 30 cm or 3 cm × 20 cm 4 cm × 15 cm or 5 cm × 12 cm or 6 cm × 10 cm

8. Fresh Farms Dairy sells milk in a carton in the shape of a cuboid with internal dimensions 6cm by 4

cm by 10 cm. JANUARY 2011 Question 3b

a. Calculate, in cm3, the volume of milk in each

carton. Answer: Volume = 240 cm3

b. A recipe for making ice-cream requires 3 litres of milk. How many cartons of milk should be bought to

make the ice-cream? Answer: 13 cartons

c. One carton of milk is poured into a cylindrical cup of internal diameter 5 cm. What is the height of the

10 cm

6 cm

(56)

milk in the cup? Give your answer to 3 significant

figures. Use . Answer: Height = 12.2 cm

9. The diagram below, not drawn to scale, shows a cuboid with length 13 cm, width 4 cm and height h

cm. JANUARY 2012 Question 4c

a. State, in terms of h, the area of the shaded face of

the cuboid. Ans. Area of shaded region = 4h cm2

b. Write an expression, in terms of h, for the volume

of the cuboid. Answer: Volume = 52h cm3

(57)

c. If the volume of the cuboid is 286 cm3, calculate

the height, h, of the cuboid. Ans.: Height = 5.5 cm

10. Water is poured into a cylindrical bucket with a base area of 300 cm2. If 4.8 litres of water was poured into the bucket, what is the height of the water in the bucket?

References

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