Worksheet 10A (page 10.1)
1. (a) Area of X
Area of Y
Area of Z
\ Area of the shaded region
(b) Area of X
Area of Y
Area of Z
\ Area of the shaded region
(c) Area of ABCD
Area of EFGH
\ Area of the shaded region
(d) Area of ABCD
Area of EFGN
Area of MGHL
Area of KHIJ
\ Area of the shaded region
2. (a) Area of parallelogram ABCD
Area of parallelogram EFGD
\ Area of the shaded region
(b) Area of trapezium ABEF
Area of trapezium BCDE
\ Area of the shaded region
(c) Area of square ABGH
Area of trapezium BCFG
Area of trapezium CDEF
\ Area of the shaded region
(d) Area of rectangle ABCD
Area of DAED
Area of DAFB
Area of DBGC
Area of DCHD
\ Area of the shaded region
3. (a) Area of DABC
Area of DABD
Area of DABE
\ Area of the shaded region
(b) Area of parallelogram ABCD
Area of parallelogram EFGH
Area of square PQRS
\ Area of the shaded region
4. (a) Area of parallelogram ABCD
(b) Area of parallelogram ABCD
Worksheet 10B (page 10.7)
1. (a)
(b)
(c)
(d)
2. (a)
(b)
3. (a)
(b)
\ Area of quadrilateral BCED
Worksheet 10C (page 10.11)
1. (a) Circumference
(b) Let dcm be the diameter of the circle.
\ The diameter of the circle is 2.5cm.
2. (a) Perimeter of the figure
=Perimeter of semi-circle
(b) Perimeter of the figure
=Perimeter of semi-circle AB+perimeter of
semi-circle
3. Perimeter of the swimming pool
4. (a) Let dcm be the diameter of the circle.
\ The diameter of the circle is 49cm.
(b) Radius
5. Let rcm be the radius of wheel A.
Distance travelled by wheel B
Distance travelled by wheel A
\
\ The radius of wheel A is 40cm.
Worksheet 10D (page 10.15)
1. (a) Area
(b) Let dcm be the diameter of the circle.
\ The diameter of the circle is 8cm.
2. Let rcm be the radius of the circle.
\ The radius of the circle is 3cm.
Area
3. Area of the semi-circle
Area of the circle
\
\
4. (a) (i) Area of the inner circle
(ii) Area of the outer circle
\ Area of the ring
(b) Region B
(c) Let rcm be the radius of the inner circle.
Area of the inner circle
Area of the ring
In order to have an equal chance of hitting the two regions, area of the inner circle =area of the ring.
\
(corr. to 1 d.p.)
\ When the radius of the inner circle is
35.4cm, there will be an equal chance
of hitting the two regions.
Worksheet 10E (page 10.19)
1. (a) Area of sector
(b) Arc length
2.
Perimeter
3.
Area of sector
4. Length of
Length of
\ Total length of the crash barriers
(corr. to the nearest 0.1m)
5. Area of sector OAD
Area of sector OBC
\
(corr. to 3 sig. fig.)
Worksheet 10F (page 10.23)
1. Base area
\ Volume of the prism
2. Base area
\ Volume of the cylinder
3. Volume of the gold bar
Volume of a gold coin
Number of gold coins
4. Based on the outer dimensions of the bookshelf, the volume of the bookshelf
Total volume of the space available inside the bookshelf for storage
\ Volume of the wooden board used
5. (a) Capacity of the copper cup
(b) Outer base radius of the copper cup
Outer height of the copper cup
Volume of the copper cup
Volume of the cylindrical copper bar
\ It is enough to cast the copper cup by
melting the copper bar.
Worksheet 10G (page 10.27)
1. (a) In DABC,
(Pyth. theorem)
Total area of the upper and lower bases
Lateral surface area
\
(b) Total area of the upper and lower bases
Curved surface area
\
(c) Total area of the upper and lower bases
Curved surface area
\
2. (a) For cylinder A,
\ The base radius of cylinder A is.
For cylinder B,
\ The base radius of cylinder B is.
(b) Volume of cylinder A
Volume of cylinder B
\ Cylinder A has a larger volume.
3. Surface area covered by cream in the top layer
Surface area covered by cream in the middle layer
Surface area covered by cream in the bottom layer
\ Total surface area covered by cream
Worksheet 10H(page 10.31)
1. (a) (i) Upper limit of the length
Lower limit of the length
(ii) Upper limit of the width
Lower limit of the width
(b) Upper limit of the area of the poster
Lower limit of the area of the poster
\ Area of the poster
2. (a) (i) Upper limit of AB
Lower limit of AB
(ii) Upper limit of DC
Lower limit of DC
(iii) Upper limit of DE
Lower limit of DE
(b) Upper limit of the area of the trapezium
Lower limit of the area of the trapezium
\ Area of the trapezium
3. (a) (i) Upper limit of the base radius
Lower limit of the base radius
(ii) Upper limit of the height
Lower limit of the height
(b) Upper limit of the volume of the cylinder
Lower limit of the volume of the cylinder
\ Volume of the cylinder
4. (a) (i) Upper limit of the thickness
Lower limit of the thickness
(ii) Upper limit of the length
Lower limit of the length
(iii) Upper limit of the width
Lower limit of the width
(b) Upper limit of the volume of the stack of paper
Lower limit of the volume of the stack of paper
\ Volume of the stack
of paper
Build-up Exercise 10A (page 10.35)
1. (a) Area
(b) Area
(c) Area
(d) Area
(e) Area
(f) Area
2. (a)
Area of ABMN
Area of NFGH
Area of EMCD
\ Area of the shaded region
(b)
Area of ABCL
Area of KDEJ
Area of IFGH
\ Area of the shaded region
(c)
Area of ABKJ
Area of CDEF
Area of GHIK
\ Area of the shaded region
(d) Area of ABCD
Area of EFGH
\ Area of the shaded region
(e)
Area of GBCD
Area of AGEF
Area of WXYZ
\ Area of the shaded region
(f)
Area of ABGH
Area of CDEF
Area of WXYZ
\ Area of the shaded region
3. (a)
Area of parallelogram APIJ
Area of parallelogram PBGH
Area of parallelogram BQFG
Area of parallelogram QCDE
\ Area of the shaded region
(b) Area of DABD
Area of DCBD
\ Area of the shaded region
(c) Area of DABC
Area of rectangle DEFG
\ Area of the shaded region
4. (a) Area of trapezium ABCD
Area of DADE
\ Area of the shaded region
(b) Area of DABE
Area of trapezium BCDE
\ Area of the shaded region
(c) Area of trapezium ABCD
Area of trapezium EFGH
\ Area of the shaded region
5. (a) Area of rectangle ABCD
Area of DBCE
Area of DBCF
\ Area of the shaded region
(b) Area of parallelogram ABCD
Area of parallelogram AFED
Area of DADH
\ Area of the shaded region
(c) Area of trapezium ABCD
Area of DCDE
Area of DCDF
\ Area of the shaded region
6.
Area of the shaded region
\
7. (a) Area of ABCD
(b) (Pyth. theorem)
(c) Area of ABCD
8. Let.
Area of DMPQ
Area of trapezium MNSP
Area of DNRS
\ Area of quadrilateral PQRS
Build-up Exercise 10B (page 10.37)
9. (a)
(b)
10. (a)
(b)
11.
12.
\
13. (a) Area of ABCDEFGH
(b)
\ Area of ABCDEFGH is,
Area of IJKLMNOP is.
14. (a) Area of DABC:Area of DADE
(b)
15.
16.
Build-up Exercise 10C (page 10.39)
17. / Radius / Diameter / Circumference5cm / 10cm / 31.4cm
12.5cm / 25cm / 78.5cm
10cm / 20cm / 62.8cm
17.5cm / 35cm / 109.9cm
25cm / 50cm / 157cm
42.5cm / 85cm / 266.9cm
18. (a) Perimeter
(b) Perimeter
(c) Perimeter
19. (a) Perimeter
(b) Perimeter
(c) Perimeter
20. (a) Perimeter
(b) Perimeter
(c) Perimeter
21. Difference in their circumferences
22. Distance travelled
(corr. to 1 d.p.)
23. Distance moved
24. Let rm be the radius of the park.
(corr. to 1 d.p.)
\ The radius of the park is 49.7m.
25. Circumference of the base of the can
Let dcm be the diameter of the base of the can.
(corr. to 1 d.p.)
\ The diameter of the base of the can is 10.5cm.
26. Distance travelled by the coin per second
(corr. to 1 d.p.)
\ The speed of the coin is 22.6cm/s.
27. Letandbe the diameters of the larger and smaller circles respectively.
\ The ratio of the diameter of the larger
circle to that of the smaller circle is.
28. Distance travelled by the car per hour
(corr. to 1 d.p.)
\ The speed of the car is 49.8km/h.
29. Let,andbe the respective radii of the three circles, then.
\
\
\ The ratio of the radii of the three circles is
.
30. Base diameter
(corr. to 1 d.p.)
Base diameterLength of each side of the square
\ The square metal plate cannot be put into
the container.
Build-up Exercise 10D (page 10.41)
31. / Radius / Diameter / Area5cm / 10cm / 78.5cm2
8cm / 16cm / 201.1cm2
6cm / 12cm / 113.1cm2
15cm / 30cm / 706.9cm2
3.7cm / 7.4cm / 43cm2
5.5cm / 11.0cm / 95.2cm2
32. (a) Area
(b) Area
(c) Area
33. (a) Area
(b) Area
(c) Area
34. Area ofof the circle
Area of DAOB
\ Area of the shaded region
(corr. to 1 d.p.)
35. Area
(corr. to 1 d.p.)
36. Let rcm be the radius of the discus.
(corr. to 1 d.p.)
\ The radius of the discus is 10.6cm.
37.
(corr. to 1 d.p.)
38.
Area of the shaded region in the figure
=Area of the square ABCD-Area ofof the circle
\ Area required
(corr. to 1 d.p.)
39. Let r be the original radius of the circle.
Original area
New radius
New area
Percentage decrease in the area of the circle
40. Letandbe the diameters of the smaller and larger cakes respectively.
\ The ratio required is.
41. (a) Ratio of the areas
(b) Letbe the area of the smaller circle, then the area of the larger circle is .
\ The areas of the smaller circle and the
larger circle areand
respectively.
42. Let rcm be the radius of the circle.
\ The radius of the circle is.
Area
(corr. to 1 d.p.)
43. Let rm be the radius of the circular lawn.
\ The radius of the circular lawn is.
Length of the fences
(corr. to 1 d.p.)
44. Let xm be the height of the rectangle.
\ The height of the rectangle is 2.5m.
Height of the door
45. Area of the wooden frame
(corr. to 1 d.p.)
46. (a) Radius
(b) (Length of the side)
(Pyth. theorem)
Length of the side
(corr. to 3 sig. fig.)
(c) Area of the shaded region
(corr. to 3 sig. fig.)
47. (a) (i) Area of region A
(ii) Area of region B
=Area of the square-Area of region A
(b) Area of the shaded region
=Area of the square-2´Area of region B
Build-up Exercise 10E (page 10.45)
48. (a) Length of
(corr. to 3 sig. fig.)
(b) Length of
(corr. to 3 sig. fig.)
(c) Length of
(corr. to 3 sig. fig.)
49. (a) Area of sector AOB
(corr. to 3 sig. fig.)
(b) Area of sector AOB
(corr. to 3 sig. fig.)
(c) Area of sector AOB
(corr. to 3 sig. fig.)
50. (a)
(b)
(c)
51. (a)
(b)
(c)
52. Length of arc AB
(corr. to 3 sig. fig.)
53. Area of sector AOB
(corr. to 3 sig. fig.)
54. (a) Perimeter of the sector
(corr. to 3 sig. fig.)
(b) Perimeter of the sector
(corr. to 3 sig. fig.)
(c) Perimeter of the sector
(corr. to 3 sig. fig.)
55. Area of the shaded region
(corr. to 3 sig. fig.)
56. Area of ABCD
=Area of sector OBC-Area of sector OAD
(corr. to 3 sig. fig.)
57. (a) Area of DOAB
Area of the shaded region
(corr. to 3 sig. fig.)
(b) (Pyth. theorem)
Area of the shaded region
(corr. to 3 sig. fig.)
58. (a) Join CD.
In DACD,
(Pyth. theorem)
\ Area of DABC
\ Area of sector FAD
\ Area of the shaded region
(corr. to 3 sig. fig.)
(b) Percentage required
(corr. to 3 sig. fig.)
59. (a) Let, then, .
Area of sector OAB
(corr. to 3 sig. fig.)
(b)
Area of sector OAB
60. (a)
\
\
(b) Letbe the area of sector OAC.
\ The area of sector OAC is.
61. Length of the iron wire required