Supp 2E10 Bslau.weebly.com/uploads/1/3/3/0/13308739/supp_2e10_b.pdf · 2018. 10. 4. · A B D E 24 cm 15 7cm Q M N R P S ... If the area of the sitting room on the floor plan is 8.1

10.35

© 2009 Chung Tai Educational Press. All rights reserved.

1. Find the area of each of the following figures.

(a)

Rectangle

2 cm

6 cm (b) 9 cm

Square

(c)

5 cm

6 cm

Triangle

(d)

Parallelogram

13 cm

8 cm10 cm

(e)

Triangle

69 cm

20 cm29 cm

52 cm

(f)

Trapezium

10 cm

12 cm

15 cm

13 cm

2. Each of the following figures is formed by rectangles. Find the area of the shaded region in each of the following figures.

(a)

6 cm

8 cm

10 cm

2 cm

3 cm6 cm

8 cm

5 cm

B C

A H

GD

F

E

(b)

5 cm12 cm

12 cm

4 cm

3 cm

20 cm

4 cm 4 cm

A L I H

B C F G

K

D

J

E

(c) 10 m2 m

2 m

6 m

3 m

3 m6 m

6 m

A J

IH

ED

BC F G

(d)

4 cm

7 cm

6 cm 12 cm

A D

B C

F G

E H

(e)

32 cm

7 cm

8 cm

12 cm

8 cm

25 cmA F

E

CB

D W

Z

Y

X

(f) 10 cm

8 cm

2 cm

2 cm

4 cm

1 cm

A H

B GC F

YX

ZW

D E

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3. Find the area of the shaded region in each of the following figures.

(a) 3.5 cm

8 cm

3.5 cm

1.5 cm

2 cm

2 cm

1.5 cm

A J

H

B

C D

FE

GI

(b) A

B D

C

10 cm

9 cm

6 cm

E

(c)

E F

D

B

G AC 5 cm3 cm

5 cm

12 cm

12 cm16 cm


(a)

12 cm

A B

D C

8 cm

5 cm

12 cm

13 cm

E

(b)

D

B E

A

C

20 cm

24 cm

25 cm

18 cmF

G

(c) 8 cm

A

B C

D

E H

GF

15 cm

12 cm

8 cm

4 cm

6 cm


(a)

BE and CD meet at F.

C

F

G

E

B

DA

16 cm10 cm

20 cm

30 cm

(b) A DI

B C FG E14 cm

20 cm

H

15 cm

AF and CD meet at H.

(c)

D G C

E A

F

B

18 cm

AD and CE meet at F.

40 cm

50 cm

20 cm

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6. In the figure, if the area of the shaded region is 2cm 31 , find the

value of x.

7. In the figure, ABCD is a parallelogram. E is a point on BC such that .BCDE ⊥ ,CFBF ⊥ cm 15 =AB , cm 7 =BF and

cm 24 =CF .

(a) Find the area of ABCD.

(b) Find the length of BC.

(c) Find the length of DE. 8. The figure shows quadrilateral PQRS. If M and N are points on QR

such that cm 6 =PM , cm 10 =SN , cm 11 =QN and cm 14 =RM ,

find the area of quadrilateral PQRS.

[ Hint: Let MN = x cm. ]

9. Find the unknown in each of the following pairs of similar figures. (a)

Area = 18 cm2 Area = x cm2

12 cm

4 cm

(b)

Area = 2 cm2 Area = y cm2

3.2 cm

2 cm

P D E Q

GF

BC

A

2 cm

3 cm

2 cm

2 cm

x cm

2 cm

10 cm

FBA

CD

E

24 cm

7 cm15 cm

NMQ R

P

S

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10. Find the unknown in each of the following pairs of similar figures.

(a)

1.2 cm

x cm

Area = 4 cm2 Area = 9 cm2

(b)

Area = 50 cm2 Area = 18 cm2

7.5 cm

y cm

11. In the figure, ABCD and AFGE are two similar figures. If the

area of AFGE is 2cm 56 , find the area of ABCD.

12. In the figure, ABCDEF and APQRST are two similar figures, their respective areas are

2cm 125 and 2cm 20 . Find the length

of PB.

13. In the figure, ABCDEFGH and IJKLMNOP are two similar figures, their total area is .cm 25.111 2

Let 2cm x be the area of

IJKLMNOP.

(a) Express the area of ABCDEFGH in terms of x.

(b) Find the area of ABCDEFGH and the area of IJKLMNOP.

B C

A E

G

D

F

8 cm

4 cm

A P B

CD

E F

TS

R Q

6 cm

D E

F GB C

3 cm

I HA P

JKN

LM

O

3 cm10 cm

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14. In the figure, ADEABC ΔΔ ~ . The area of the shaded region and the area of ΔABC are

2cm 64 and 2cm 36 respectively.

(a) Find the ratio of the area of ΔABC to that of ΔADE.

(b) Find the length of AB.

15. Two pieces of iron wire of different lengths are bent into two similar polygons in the star shape, where the ratio of the lengths of the two pieces of wire is 6 : 11. If the area of the smaller star is

2cm 72 , find the area of the larger star.

16. The scale of the floor plan of a flat is 1 cm to 1.5 m. If the area of the sitting room on the floor plan is 2cm 1.8 , find its actual area.

[ In this exercise, give your answers correct to 1 decimal place if necessary. ]

17. Complete the following table. (Take 14.3=π .)

Radius Diameter Circumference

5 cm

12.5 cm

20 cm

35 cm

157 cm

266.9 cm

A

B C

D E

6 cm

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18. Find the perimeter of each of the following semi-circles. (Express your answers in terms of π.)

(a)

A B12 cm

(b) A

B

42 cm

(c) OA B

5 cm

19. The following figures are formed by semi-circles, find the perimeter of each figure. (Express your answers in terms of π.)

(a)

A B C5 cm 5 cm

(b) A

B

C

7 cm11 cm

(c)

4 cm4 cm6 cmA

B

CD

20. Find the perimeter of each of the following figures. (Express your answers in terms of π.)

(a)

The figure is formed bysemi-circles and a straight line.

A CB

6 cm10 cm

(b)

The figure is formed bysemi-circles and a straight line.

B

A

C

2 cm

4 cm

(c)

The figure is formed byquadrants and straight lines.

O

A

B

C D15 cm12 cm

21. Given that the diameters of two circles are 14 cm and 16 cm respectively, what is the difference in

their circumferences? (Express your answer in terms of π.)

22. The diameter of a wheel of a bicycle is 0.6 m. Find the distance travelled by the bicycle in 20 revolutions of the wheel.

23. The length of the minute-hand of a clock is 12 cm. Find the distance moved by the tip of the minute-hand in 45 minutes. (Express your answer in terms of π.)

24. Terry jogged around a circular park. Suppose he had completed 4 laps with a total distance of 1 250 m, find the radius of the park.

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25. A rope of 198 cm long can wrap around a cylindrical can 6 times. What is the diameter of the base of the can?

26. A coin with the radius of 1.2 cm makes 3 revolutions per second on the ground. Find the speed of this coin. (Express your answer in cm/s.)

27. The ratio of the circumferences of two circles is 7 : 5. What is the ratio of their diameters?

28. The diameter of a car wheel is 48 cm. If the wheel makes 550 revolutions per minute, find the speed of the car. (Express your answer in km/h.)

29. The ratio of the circumferences of three circles is 7a : 5b : 4c. What is the ratio of their radii?

30. The height and the circumference of the base of a right cylindrical container are 20 cm and 30 cm respectively. Can a square metal plate with the sides of 10 cm each be put into the container? Explain briefly.

[ In this exercise, give your answers correct to 1 decimal place if necessary. ]

31. Complete the following table.

Radius Diameter Area

5 cm

8 cm

12 cm

30 cm

43 cm2

95.2 cm2

10.42


32. The following figures are formed by semi-circles and straight lines, find the area of each figure. (Express your answers in terms of π.)

(a)

B

A

D

10 cm

8 cm C

(b)

A B C D

4 m1 m 1 m

(c) 4 cm

3 cm

AB C

33. The following figures are formed by semi-circles, find the area of each figure. (Express your answers in terms of π.)

(a)

A4 cm

B C4 cm

(b)

A DB C

4 cm6 cm 6 cm (c)

ADCB

8 cm6 cm 4 cm

34. The following figure is formed by a quadrant and an isosceles right-angled triangle. Find the area of the shaded region.

3 cm

A O

B

3 cm

35. The diameter of a circular flying disc is 24 cm, find its area.

36. The area of a discus is 2cm 350 , find its radius.

10.43


37. The figure is formed by a quadrant, a semi-circle and a straight line. If the area of the shaded region is 2cm 100 , find the value of x.

x cm

38. The following figure is formed by quadrants and a square. Find the area of the shaded region.

2 cm

A

2 cm

B C

D

39. If the radius of a circle decreases by 5%, what is the percentage decrease in the area of the circle?

40. The base areas of two cylindrical cakes are in the ratio of 9 : 16. Find the ratio of their base diameters.

41. In the figure, the ratio of the radii of two circles is 7 : 9.

(a) Find the ratio of the area of the smaller circle to that of the larger circle.

(b) If the area of the shaded region is 2cm 48 , find the respective areas of the smaller circle and the

larger circle.

42. It is given that the length of a necklace is 50 cm. What is the area of the circle formed by the necklace?

43. A circular lawn with the area of 2m 42 is surrounded by fences. Find the length of the fences.

10.44


44. In the figure, the door is formed by a semi-circle and a rectangle. If its area is 2m )318.0( +π , find its

height.

0.6 m

Height

45. In the figure, the width of the wooden frame is 1 cm. Find its area.

1 cm

11.43 cm

15.24 cm

A quadrant

46. The figure is formed by two squares and a circle.

12 cm

(a) Find the radius of the circle. (b) Find the length of the side of the smaller square. (Give your answer correct to 3 significant

figures.) (c) Find the area of the shaded region. (Give your answer correct to 3 significant figures.)

10.45


47. Figure I and Figure II are formed by squares and quadrants.

A

B

10 cm 10 cm

Figure I Figure II

(a) In Figure I, (i) find the area of region A. (ii) find the area of region B.

(b) Hence, find the area of the shaded region in Figure II. (Express your answers in terms of π.)

[ In this exercise, give your answers correct to 3 significant figures if necessary. ]

48. Find the length of BA

in each of the following figures.

(a)

100°

A

BO

3 cm

3 cm

(b)

210°

A

B

2 cm2 cm

O

(c)

330°A

B

5 cmO

5 cm

49. Find the area of sector AOB in each of the following figures.

(a)

35°

A

B

6 cm

O6 cm

(b)

115°

O

4.5 cm

A

4.5 cmB

(c)

260°

O3 cm

A

B

3 cm

10.46


50. Find the value of x in each of the following figures.

(a)

Ox

B

A

12 cm

12 cm

8π

3cm

(b)

O

x

A

B

40 cm40 cm

48π cm (c)

Area = 224π cm2

Ox

A

B

16 cm

16 cm

51. Find the value of x in each of the following figures.

(a)

A

O B

x cm

x cm

11π cm

132°

(b)

200°

O BA

x cmx cm

30π cm (c)

Area = 72π cm2

320°O

BA

x cmx cm

52. An arc AB of a circle with the diameter of 25 cm subtends an angle of 45° at the centre. Find the

length of arc AB.

53. An arc AB of a circle with the diameter of 7 cm subtends 66° at the centre at O. Find the area of sector AOB.

54. Find the perimeter of each of the following sectors.

(a) Y

OX 2 cm

2 cm

40°

(b)

O

Y

X 7 cm7 cm

160°

(c)

O

Y

X 1.2 cm

210°

1.2 cm

10.47


55. In the figure, O is the centre of arc APC and arc BQD. AEB and CFD are semi-circles. It is given that ,120°=∠BOD cm 6 =OA and cm 2 =AB . Find the area of the shaded region.

56. The figure shows a paper fan, where ,cm 8 ==ODOA

cm 15 == DCAB and °=∠ 108AOD . Find the area of ABCD.

57. In the figure, O is the centre, the radius is 8 cm, °=∠ 90AOB .

(a) Find the area of the shaded region.

(b) Find the perimeter of the shaded region.

58. The figure shows an equilateral triangle ABC with sides of 10 cm each. D, E and F are mid-points of the sides of the triangle. A, B and C are the centres of the arcs DF

, ED

and FE

respectively.

(a) Find the area of the shaded region.

(b) Find the percentage of the shaded area in the figure.

120°

BA

C

O

D

F

EP

Q

B

O

C

D A

8 cm

A B

O

A D B

EF

C

10.48


59. An iron wire of length 100 cm is bent into a sector OAB as shown in the figure.

(a) If °=∠ 30AOB , find the area of sector OAB.

(b) If cm 20 =OA , find the area of sector OAB.

60. In the figure, OAC and OBD are two similar sectors. The area of the shaded region is

2cm 30 π . The length of OA is 4 times that of AB.

(a) Find OAOB : .

(b) Find the area of sector OAC. (Express your answer in terms of π.)

61. The figure is formed by arc ACB and arc ADB, where O and P are the centres of arc ACB and arc ADB respectively. Is a piece of iron wire with the length of 40 cm enough to form the figure? Explain briefly.

62. In the figure, rectangle PQRS is formed by a wire. The wire is now bent into sector OAB.

(a) Find the perimeter of sector OAB.

(b) If the length of BA

is 10 cm, find AOB∠ . (Express your answer in terms of π.)

(c) Is the area of sector OAB equal to the area of rectangle PQRS? Explain briefly.

A B

O

A BO

C

D

4 cmC

B

A

DP

70°

6 cm

120°O

O

A B

RQ

P S4 cm

9 cm

10.49


63. In the figure, ABC is an equilateral triangle with sides of 20 cm each. The centres of CPB

, CQA

and

BRA

are A, B and C respectively. Find the area of the shaded region.

20 cm 20 cm

B C

P

A

R Q

20 cm

64. In the figure, OAB and PCD are sectors, Chris thought that 2)(

sector of area sector of area

OBPD

OABPCD

= , do you

agree? Explain briefly.

B

A

D

C

O P

16 cm

16 cm8 cm

8 cm20° 40°


65. Complete the following table.

Base area of prism Height of prism Volume of prism

10 cm2 5 cm

25 cm2 4 cm

150 cm2 600 cm3

12 cm2 180 cm3

25 cm 900 cm3

60 cm 1 080 cm3

10.50


66. Find the volume of each of the following prisms.

(a) 8 cm6 cm

12 cm

(b)

7 cm

6 cm

11 cm

10 cm

(c)

14 cm

3 cm10 cm

67. The following are cylinder A and cylinder B. Find the difference in their volumes. (Express your answer in terms of π.)

Cylinder A Cylinder B

4 m

O

2 m

4 mO

2 m

68. A cylindrical cup with the base radius of 5 cm is filled with water. If 80 cubes with sides of 1 cm each

are immersed into the water without overflow,

(a) find the volume of a cube.

(b) find the rise in the water level.

69. The base diameter and the capacity of a cylindrical can are 6.5 cm and 3cm 330 respectively. Find the

height of the can.

70. A cylindrical metal bar with the radius of 3 cm and length of 5 cm is melted and recast into a pipe as shown below. Find the length of the pipe.

3 cm

1 cmO

10.51


71. Find the volume of each of the following prisms. (a)

4 cm

16 cm

10 cm

8 cm

12 cm

(b)

6 cm

10 cm

16 cm10 cm

24 cm

(c)

3 cm

2 cm

2 cm

2 cm2 cm

2 cm

5 cm

72. There are 50 rectangular copper bars with dimensions .cm 10mm 5mm 4 ×× They are melted and recast

into a large cuboid with the sides of its square base of 1 cm each. Find the height of the large cuboid.

73. The figure shows a copper coin with the diameter of 24 mm. In the centre of the coin, there is a square hole with the sides of 5 mm each. If the total volume of 50 copper coins is

3cm 24 , find the thickness of each copper coin.

24 mm

5 mm

74. The figure shows the uniform cross-section of an L-shaped aluminium plate. Each aluminium plate is

120 cm long.

40 mm

40 mm

2 mm

2 mm

(a) Find the volume of a piece of L-shaped aluminium plate in

3cm .

(b) It is known that the density of aluminium is 3g/cm 7.2 . Is it enough to produce 20 pieces of

L-shaped aluminium plate with 10 kg of aluminium? Explain briefly.

10.52


75. The figure shows a spiral staircase with 4 steps. Each step is 15 cm high. The uniform cross-section of each step is a sector with the angle at the centre of 30° and radius of 40 cm. Find the volume of the spiral staircase.

15 cm

15 cm

15 cm

15 cm

40 cm30°

76. Water flows through a pipe with the inner diameter of 16 cm at a speed of 0.8 m/s.

(a) Find the volume of water flowing out from the pipe per second. (Express your answer in terms of π.)

(b) The height and the base radius of a cylindrical tank are 1 m and 2 m respectively. Can the tank be fully filled by the above pipe in 15 minutes? Explain briefly.

77. If both the base radius and the height of a cylinder increase by 10%, find the percentage increase in its volume.


78. Find the total surface area of each of the following solids. (a)

Cube

2 cm2 cm

2 cm

(b)

Cuboid

4 cm6 cm

1 cm

(c)

Cylinder

20 cm

14 cmO

10.53


79. Find the total surface area of each of the following prisms.

(a)

16 cm

10 cm

10 cm

10 cm

6 cm (b) 5 cm

10 cm

12 cm4 cm

4 cm5 cm

(c) 12 cm

4 cm

3 cm

4.2 cm

80. A metal cuboid with the length of 16 cm, width of 8 cm and height of 4 cm is melted and recast into a

cube. Find the total surface area of the cube.

81. The base radius and the height of a cylinder are r cm and h cm respectively. If the sum of the areas of the two bases is equal to the curved surface area of the cylinder, find r : h.

82. The figure shows a cylindrical can with the diameter of 8 cm and capacity of 3cm 600 . A rectangular

packing paper is perfectly fit on the curved surface of the can. Find the area of the packing paper.

8 cm

83. The length, width and height of a room are 8 m, 6 m and 2.5 m respectively. The total area of a door

and a window occupies 51

of the area of the walls in the room. If the ceiling and the walls are to be

painted,

(a) find the total painted area.

(b) Given that the capacity of a tin of paint is 2 L and each L of paint can paint an area of 2m 6 , are

10 tins of paint enough to paint the room? Explain briefly.

10.54


84. (a) Figure I is formed by two semi-circles with the diameters of 3 cm each and a rectangle with dimensions of cm 6cm 3 × . Find the area of Figure I.

(b) Figure II shows a candy can with the height of 10 cm, and its uniform cross-section is congruent to Figure I. Given that one of its bases and the lateral surface are made of metal which cost 0.8¢/cm2, and the other base is a plastic cover which cost 5¢ each. Find the cost to produce 1 000 candy cans. (Give your answer correct to the nearest dollar.)

3 cm 10 cm

6 cm

Figure I

Figure II 85. Figure I and Figure II show two containers in the shapes of a cylinder and a square prism respectively.

Both the containers are with lids, their heights are both 10 cm, and their volumes are both 500 cm3. If the material cost of making the containers is 0.1¢/cm2, which container has a lower material cost? Explain briefly.

Figure I Figure II

86. The diameter of a circle is 3.4 cm, correct to 2 significant figures.

(a) Find the upper limit and lower limit of the diameter.

(b) Find the possible range of the circumference. (Express your answer in terms of π.)

10.55


87. The length and width of the cover of a book are 25 cm and 18 cm respectively, correct to the nearest cm.

(a) (i) Find the upper limit and lower limit of the length of the cover.

(ii) Find the upper limit and lower limit of the width of the cover.

(b) Find the possible range of the area of the cover.

88. The figure shows ΔABC, where cm 4.19 =AD and ,cm 3.24 =BC correct to 3 significant figures.

A

B CD

(a) (i) Find the upper limit and lower limit of AD.

(ii) Find the upper limit and lower limit of BC.

(b) Find the possible range of the area of ΔABC.

89. The figure shows a prism with a trapezium base, where ,m 4.2 =AB ,m 2.2 =AD m 0.3 =DC and

m 2.3 =AF , correct to 1 decimal place.

A

C

B

H

GF

E

D

(a) (i) Find the upper limit and lower limit of AB.

(ii) Find the upper limit and lower limit of AD.

(iii) Find the upper limit and lower limit of DC.

(iv) Find the upper limit and lower limit of AF.

(b) Is it possible for the actual volume of the prism to be 3m 21 ? Explain briefly.

10.56


90. The figure shows a pentagon ABCDE, where ,cm 10 =AB ,cm 8 =BC cm 26 =CD and cm 24 =AE ,

correct to the nearest cm.

A

B

C D

E

(a) Find the lower limit of the area of pentagon ABCDE.

(b) If the actual area of pentagon ABCDE is 2cm x , find the range of values of x.

91. The figure shows the floor plan of a flat.

A F

DE

BC

(a) In the floor plan, measure the lengths of AB, AF, ED and CD. (Give your answers correct to the nearest 0.1 cm.)

(b) Given that the scale of the floor plan is 1 cm : 1.2 m, can the area of the flat be 2m 32 ? Explain

briefly.

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Supp 2E10 Bslau.weebly.com/uploads/1/3/3/0/13308739/supp_2e10_b.pdf · 2018. 10. 4. · A B D E 24 cm 15 7cm Q M N R P S ... If the area of the sitting room on the floor plan is 8.1