Answers to practice exercises 351
Chapter 25
Exercise 96 (page 221)
1. p = 105 ◦ , q = 35 ◦ 2. r = 142 ◦ , s = 95 ◦
3. t = 146
◦
Exercise 97 (page 225)
1. (i) rhombus (a) 14 cm
2 (b) 16 cm (ii) parallelogram
(a) 180 mm 2 (b) 80 mm (iii) rectangle (a) 3600 mm 2
(b) 300 mm (iv) trapezium (a) 190 cm 2 (b) 62.91 cm
2. 35.7 cm 2 3. (a) 80 m (b) 170 m 4. 27.2 cm 2
5. 18 cm
6. 1200 mm
7. (a) 29 cm 2 (b) 650 mm 2
8. 560 m 2
9. 3.4 cm
10. 6750 mm 2
11. 43.30 cm 2
12. 32
Exercise 98 (page 226)
1. 482 m 2
2. (a) 50.27 cm 2 (b) 706.9 mm 2 (c) 3183 mm 2
3. 2513 mm 2
4. (a) 20.19 mm (b) 63.41 mm
5. (a) 53.01 cm 2 (b) 129.9 mm 2
6. 5773 mm 2
7. 1.89 m 2
Exercise 99 (page 228)
1. 1932 mm 2 2. 1624 mm 2 3. (a) 0.918 ha (b) 456 m
Exercise 100 (page 229)
1. 80 ha
2. 80 m 2
3. 3.14 ha
Chapter 26
Exercise 101 (page 231)
1. 45.24 cm 2. 259.5 mm 3. 2.629 cm 4. 47.68 cm
5. 38.73 cm 6. 12730 km 7. 97.13 mm
Exercise 102 (page 232)
1. (a)
π
6
(b)
5π
12
(c)
5π
4
2. (a) 0.838 (b) 1.481 (c) 4.054
3. (a) 210 ◦ (b) 80 ◦ (c) 105 ◦
4. (a) 0 ◦ 43 (b) 154 ◦ 8 (c) 414 ◦ 53
Exercise 103 (page 234)
1. 113 cm 2
2. 2376 mm 2
3. 1790 mm 2
4. 802 mm 2 5. 1709 mm 2
6. 1269 m 2
7. 1548 m 2
8. (a) 106.0 cm (b) 783.9 cm 2
9. 21.46 m 2 10. 17.80 cm, 74.07 cm 2
11. (a) 59.86 mm (b) 197.8 mm
12. 26.2 cm
13. 8.67 cm, 54.48 cm 14. 82.5
◦
15. 748
16. (a) 0.698 rad (b) 804.2 m 2
17. 10.47 m 2
18. (a) 396 mm 2 (b) 42.24%
19. 701.8 mm
20. 7.74 mm
Exercise 104 (page 237)
1. (a) 2 (b) (3, −4)
2. Centre at (3, −2), radius 4
3. Circle, centre (0, 1), radius 5
4. Circle, centre (0, 0), radius 6
Chapter 27
Exercise 105 (page 243)
1. 1.2 m 3
2. 5 cm 3
3. 8 cm 3
4. (a) 3840 mm 3 (b) 1792 mm 2
5. 972 litres
6. 15 cm 3 , 135 g
7. 500 litres
8. 1.44 m 3
9. (a) 35.3 cm 3 (b) 61.3 cm 2
10. (a) 2400 cm 3 (b) 2460 cm 2 11. 37.04 m
12. 1.63 cm
13. 8796 cm
3
14. 4.709 cm, 153.9 cm 2
15. 2.99 cm
16. 28060 cm 3 , 1.099 m 2
17. 8.22 m by 8.22 m
18. 62.5 min
19. 4 cm
20. 4.08 m 3
Exercise 106 (page 246)
1. 201.1 cm 3 , 159.0 cm 2 2. 7.68 cm 3 , 25.81 cm 2
3. 113.1 cm 3 , 113.1 cm 2 4. 5.131 cm 5. 3 cm
6. 2681 mm 3 7. (a) 268 083 mm 3 or 268.083 cm 3
(b) 20 106 mm 2 or 201.06 cm 2
8. 8.53 cm
9. (a) 512 × 10 6 km 2 (b) 1.09 × 10 12 km 3 10. 664
Exercise 107 (page 251)
1. 5890 mm 2 or 58.90 cm 2
2. (a) 56.55 cm 3 (b) 84.82 cm 2
3. 13.57 kg
4. 29.32 cm 3
5. 393.4 m 2
6. (i) (a) 670 cm 3 (b) 523 cm 2 (ii) (a) 180 cm 3
(b) 154 cm 2 (iii) (a) 56.5 cm 3 (b) 84.8 cm 2
(iv) (a) 10.4 cm
3 (b) 32.0 cm
2 (v) (a) 96.0 cm
3
Chapter 25
Exercise 96 (page 221)
1. p = 105 ◦ , q = 35 ◦ 2. r = 142 ◦ , s = 95 ◦
3. t = 146
◦
Exercise 97 (page 225)
1. (i) rhombus (a) 14 cm
2 (b) 16 cm (ii) parallelogram
(a) 180 mm 2 (b) 80 mm (iii) rectangle (a) 3600 mm 2
(b) 300 mm (iv) trapezium (a) 190 cm 2 (b) 62.91 cm
2. 35.7 cm 2 3. (a) 80 m (b) 170 m 4. 27.2 cm 2
5. 18 cm
6. 1200 mm
7. (a) 29 cm 2 (b) 650 mm 2
8. 560 m 2
9. 3.4 cm
10. 6750 mm 2
11. 43.30 cm 2
12. 32
Exercise 98 (page 226)
1. 482 m 2
2. (a) 50.27 cm 2 (b) 706.9 mm 2 (c) 3183 mm 2
3. 2513 mm 2
4. (a) 20.19 mm (b) 63.41 mm
5. (a) 53.01 cm 2 (b) 129.9 mm 2
6. 5773 mm 2
7. 1.89 m 2
Exercise 99 (page 228)
1. 1932 mm 2 2. 1624 mm 2 3. (a) 0.918 ha (b) 456 m
Exercise 100 (page 229)
1. 80 ha
2. 80 m 2
3. 3.14 ha
Chapter 26
Exercise 101 (page 231)
1. 45.24 cm 2. 259.5 mm 3. 2.629 cm 4. 47.68 cm
5. 38.73 cm 6. 12730 km 7. 97.13 mm
Exercise 102 (page 232)
1. (a)
π
6
(b)
5π
12
(c)
5π
4
2. (a) 0.838 (b) 1.481 (c) 4.054
3. (a) 210 ◦ (b) 80 ◦ (c) 105 ◦
4. (a) 0 ◦ 43 (b) 154 ◦ 8 (c) 414 ◦ 53
Exercise 103 (page 234)
1. 113 cm 2
2. 2376 mm 2
3. 1790 mm 2
4. 802 mm 2 5. 1709 mm 2
6. 1269 m 2
7. 1548 m 2
8. (a) 106.0 cm (b) 783.9 cm 2
9. 21.46 m 2 10. 17.80 cm, 74.07 cm 2
11. (a) 59.86 mm (b) 197.8 mm
12. 26.2 cm
13. 8.67 cm, 54.48 cm 14. 82.5
◦
15. 748
16. (a) 0.698 rad (b) 804.2 m 2
17. 10.47 m 2
18. (a) 396 mm 2 (b) 42.24%
19. 701.8 mm
20. 7.74 mm
Exercise 104 (page 237)
1. (a) 2 (b) (3, −4)
2. Centre at (3, −2), radius 4
3. Circle, centre (0, 1), radius 5
4. Circle, centre (0, 0), radius 6
Chapter 27
Exercise 105 (page 243)
1. 1.2 m 3
2. 5 cm 3
3. 8 cm 3
4. (a) 3840 mm 3 (b) 1792 mm 2
5. 972 litres
6. 15 cm 3 , 135 g
7. 500 litres
8. 1.44 m 3
9. (a) 35.3 cm 3 (b) 61.3 cm 2
10. (a) 2400 cm 3 (b) 2460 cm 2 11. 37.04 m
12. 1.63 cm
13. 8796 cm
3
14. 4.709 cm, 153.9 cm 2
15. 2.99 cm
16. 28060 cm 3 , 1.099 m 2
17. 8.22 m by 8.22 m
18. 62.5 min
19. 4 cm
20. 4.08 m 3
Exercise 106 (page 246)
1. 201.1 cm 3 , 159.0 cm 2 2. 7.68 cm 3 , 25.81 cm 2
3. 113.1 cm 3 , 113.1 cm 2 4. 5.131 cm 5. 3 cm
6. 2681 mm 3 7. (a) 268 083 mm 3 or 268.083 cm 3
(b) 20 106 mm 2 or 201.06 cm 2
8. 8.53 cm
9. (a) 512 × 10 6 km 2 (b) 1.09 × 10 12 km 3 10. 664
Exercise 107 (page 251)
1. 5890 mm 2 or 58.90 cm 2
2. (a) 56.55 cm 3 (b) 84.82 cm 2
3. 13.57 kg
4. 29.32 cm 3
5. 393.4 m 2
6. (i) (a) 670 cm 3 (b) 523 cm 2 (ii) (a) 180 cm 3
(b) 154 cm 2 (iii) (a) 56.5 cm 3 (b) 84.8 cm 2
(iv) (a) 10.4 cm
3 (b) 32.0 cm
2 (v) (a) 96.0 cm
3