08[A Math CD]
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Transcript of 08[A Math CD]
1 © Penerbitan Pelangi Sdn. Bhd.
Paper 2
1. Volume of the cone
= 1—3
× 22–––7
× 32 × 7
= 66 cm3
2. Volume of the right prism
= 1—2
× 12 × 5 × 10
= 300 cm3
3. Volume of the cylinder
= 22–––7
× 52 × 14
= 1100 cm3
4. Volume of the hemisphere
= 1—2
4—3
× 22–––7
× 7—2
3
= 89 5—6
cm3
5. Volume of the pyramid
= 1—3
× 6 × 6 × 8
= 96 cm3
Paper 2
1. Volume of the right prism= area of ∆PQU × PS
= 1—2
× 12 × 8 × 7
= 336 cm3
Volume of the half cylinder
= 1—2
22–––7
× 7—2
2 × 12
= 231 cm3
Volume of the solid= 336 + 231= 567 cm3
2. Volume of the prism
= 1—2
× (4 + 7) × 5 × 9
= 247.5 cm3
Volume of the cuboid= 4 × 10 × 10= 400 cm3
Volume of the solid= 247.5 + 400= 647.5 cm3
3. Volume of the quarter cylinder
= 1—4
× 22–––7
× 72 × 20
= 770 cm3
Volume of the cuboid= 20 × 7 × h= 140h cm3
Volume of the solid = 770 + 140h 1890 = 770 + 140h 140h = 1890 – 770
h = 1120140
= 8
CHAPTER
8 Solid GeometryCHAPTER
2
Mathematics SPM Chapter 8
© Penerbitan Pelangi Sdn. Bhd.
4. Volume of the cone
= 13
× 227
× 72
2 × 4
= 51 13
cm3
Volume of the hemisphere
= 12
× 43
× 227
× 73
= 718 23
cm3
Volume of the solid
= 51 13
+ 718 23
= 770 cm3
5. Volume of the pyramid
= 13
× 10 × 10 × 12
= 400 cm3
Volume of the cylinder
= 227
× 72
2 × 5
= 192.5 cm3
Volume of the remaining solid= 400 − 192.5= 207.5 cm3
6. Volume of the cuboid= 11 × 9 × 12= 1188 cm3
Volume of the cone
= 13
× 227
× 72
2 × 9
= 115.5 cm3
Volume of the remaining solid= 1188 − 115.5= 1072.5 cm3
7. (a) Volume of the cone
= 13
× 227
× 92 × 7
= 594 cm3
(b) Volume of the hemisphere
= 12
× 43
× 227
× 73
= 718 23
cm2
Volume of the solid = 594 + 718 2
3 = 1312 2
3 cm3
Paper 2
1. Volume of the half cylinder
= 12
227
× 32 × 14
= 198 cm3
Volume of the cuboid= 14 × 6 × 8= 672 cm3
Volume of the solid= 198 + 672= 870 cm3
2. Volume of the pyramid
= 13
× 8 × 8 × 9
= 192 cm3
Volume of the cube= 8 × 8 × 8= 512 cm3
Volume of the solid= 192 + 512= 704 cm3
3. Volume of the hemisphere
= 12
43
× 227
× 33
= 56 4—7
cm3
Volume of the cylinder
= 227
× 32 × 7
= 198 cm3
Volume of the solid
= 56 47
+ 198
= 254 47
cm3
3
Mathematics SPM Chapter 8
© Penerbitan Pelangi Sdn. Bhd.
4. Let the length of the cylinder be l, in cm.Volume of the cylinder
= 22–––7
× 42 × l
= 352––––7
l cm3
Volume of the two hemispheres
= 4—3
× 22–––7
× 43
= 5632–––––21
cm3
Volume of the solid = 352––––7
l + 5632–––––21
771 = 352––––7
l + 5632–––––21
352––––7
l = 771 − 5632–––––21
352––––7
l = 10 559––––––21
l = 10 559––––––21
× 7––––352
= 10 cm
5. Volume of the cylinder
= 22–––7
× 72 × 30
= 4620 cm3
Volume of the cone
= 1—3
× 22–––7
× 7—2
2 × 9
= 115.5 cm3
Volume of the remaining solid= 4620 − 2(115.5)= 4389 cm3
6. Let the radius of the cylinder be r, in cm.Volume of the cylinder
= 22–––7
× r2 × 14
= 44r2 cm3
Volume of the cone
= 1—3
× 22–––7
× r2 × 7
= 22–––3
r2 cm3
Volume of the remaining solid = 44r2 – 22–––3
r2
330 = 44r2 – 22–––3
r2
132––––3
r2 – 22–––3
r2 = 330
110––––3
r2 = 330
r2 = 330 × 3–––––––110
= 9 r = 3 cm
7. Volume of the half cylinder
= 1—2
22–––7
× 7—2
2 × 20
= 385 cm3
Volume of the right prism= area of trapezium ABGH × BC
= 1—2
× (7 + 13) × 8 × 20
= 1600 cm3
Volume of the solid= 385 + 1600= 1985 cm3
8. Let the height of the cone be h, in cm.Volume of the cone
= 1—3
× 22–––7
× 72 × h
= 154––––3
h cm3
Volume of the hemisphere
= 1—2
4—3
× 22–––7
× 73
= 2156–––––3
cm3
Volume of the solid = 154––––3
h + 2156–––––3
1129 1—3
= 154––––3
h + 2156–––––3
154h + 2156–––––––––––3
= 3388–––––3
154h + 2156 = 3388 154h = 3388 − 2156
h = 1232–––––154
= 8 cm
4
Mathematics SPM Chapter 8
© Penerbitan Pelangi Sdn. Bhd.
9. Volume of the right prism= 30 × 10= 300 cm3
Volume of the cylinder
= 22–––7
× 22 × 10
= 125 5—7
cm3
Volume of the remaining solid
= 300 − 125 5—7
= 174 2—7
cm3
10. Volume of the cylinder
= 22–––7
× 42 × 7
= 352 cm3
Volume of the hemisphere
= 1—2
4—3
× 22–––7
× 43
= 134 2–––21
cm3
Volume of the remaining solid
= 352 − 134 2–––21
= 217 19–––21
cm3
11. Let the height of the cylinder be h, in cm.Volume of the cylinder
= 22–––7
× 72 × h
= 154h cm3
Volume of the two hemispheres
= 4—3
× 22–––7
× 73
= 1437 1—3
cm3
Volume of the remaining solid = 154h − 1437 1—3
872 2—3
= 154h − 1437 1—3
154h = 872 2—3
+ 1437 1—3
= 2310
h = 2310–––––154
= 15 cm
12. Volume of the half cylinder
= 1—2
22–––7
× 52 × 14
= 550 cm3
Volume of the prism= area of trapezium ABCD × BJ
= 1—2
× (6 + 10) × 5 × 14
= 560 cm3
Volume of the solid= 550 + 560= 1110 cm3
13. Volume of the cylinder
= 22–––7
× 42 × 12
= 603 3—7
cm3
Volume of the two cones
= 2 1—3
× 22–––7
× 42 × 6
= 201 1—7
cm3
Volume of the remaining solid
= 603 3—7
− 201 1—7
= 402 2—7
cm3
14. Volume of the cylinder
= 22–––7
× 72 × 10
= 1540 cm3
Volume of the cone
= 1—3
× 22–––7
× 72 × (22 − 10)
= 616 cm3
Volume of the solid= 1540 + 616= 2156 cm3
5
Mathematics SPM Chapter 8
© Penerbitan Pelangi Sdn. Bhd.
15. Let the height of the water be h, in cm.
8 cm
4 cm
E F
GH
h
h
V
Volume of the conical container
= 1—3
× 22–––7
× 82 × 2h
= 2816–––––21
h cm3
Volume of the empty space inside the container
= 1—3
× 22–––7
× 42 × h
= 352––––21
h cm3
Volume of the water = 2816–––––21
h − 352––––21
h
821 1—3
= 2816–––––21
h − 352––––21
h
2464–––––3
= 352––––3
h
352h = 2464
h = 2464–––––352
= 7 cm
16. Volume of the half cylinder
= 1—2
22–––7
× 7—2
2 × 14
= 269.5 cm3
Volume of the right prism= area of the trapezium FGMN × EF
= 1—2
× (4 + 14) × 5 × 7
= 315 cm3
Volume of the solid= 269.5 + 315= 584.5 cm3
17. Let the height of water in the cuboid container be h, in cm.
0.5 m
1.3 mx
x2 = 1.32 − 0.52
x = 1.44 = 1.2 m
60 × 80 × h = 1—3
× 22–––7
× 502 × 120
h = 22 × 502 × 120–––––––––––––21 × 60 × 80
= 65 10–––21
cm
18. Volume of the cylinder
= 22–––7
× 7—4
2 × 8
= 77 cm3
Volume of the two discs
= 2 22–––7
× 7—2
2 × 2
= 154 cm3
Volume of the solid= 77 + 154= 231 cm3
19. EF 2 = EJ 2 + JF 2
EF = 32 + 42
= 5 cm
Volume of the prism= area of ∆EFJ × FG
= 1—2
× 3 × 4 × 8
= 48 cm3
Volume of the cuboid= 5 × 7 × 8= 280 cm3
Volume of the solid= 48 + 280= 328 cm3