year 8 maths

612
4 a 36 cm 3 b 20 m 3 c 27 mm 3 d 64 km 3
e 320 mm 3 f 24 m 3
5 a 2000 mL b 5000 L c 500 kL d 3 L
e 4 cm 3 f 50 mL g 2.5 L h 5100 cm 3
6 a 24 L b 42 L c 27 L d 18000 L
e 24000 L f 360 L
7 a i 60000000 L ii 60000 kL iii 60 ML
b 200 days
8 80 minutes
9 a 500000 m 3 b 500 ML
10 8000 kg
11 a (1, 1, 12) or (1, 2, 6) or (1, 3, 4) or (2, 2, 3)
b (1, 1, 30) or (1, 2, 15) or (1, 3, 10) or (1, 5, 6) or (2, 3, 5)
c (1, 1, 47)
12 Factors greater than 1 include only 2, 23 and 46, but 23 is
prime so you cannot find 3 whole numbers that multiply to 46.
13 9
14 a 20 b 20
c Equal, the number of cubes on the base layer is the same
as the number of squares on the base.
d If the number of cubes on the base layer is the same as
the number of squares on the base, then Ah gives h layers
of A cubes, giving the total.
e Yes, a rectangular prism could use 3 different bases.
15 a i By joining two of the same prisms together a
rectangular prism could be formed.
ii 12 units 3
b i 160 cm 3 ii 140 m 3 iii 2 cm 3 iv 112 m 3
v 48 mm 3 vi 171 cm 3
Exercise 3I
1 a i prism ii rectangle
b i prism
ii triangle
c i not a prism (pyramid)
d i not a prism (cone)
e i prism
ii square
f i not a prism (truncated pyramid)
2 a 8, 2 b 6, 1.5 c 12, 10
3 a 40 b 36 c 10 d 6280
4 a 44 m 3 b 160 cm 3 c 352 mm 3
5 a 200 cm 3 b 15 m 3 c 980 cm 3 d 60 m 3
e 270 mm 3 f 60 m 3
6 a 785.40 m 3 b 12566.37 mm 3 c 251.33 cm 3
d 7696.90 cm 3 e 461.81 m 3 f 384.85 m 3
7 a 14.137 m 3 b 14137 L
8 a 28 cm 3 b 252 m 3 c 104 cm 3
9 3 (almost 4 but not quite)
10 302.48 cm 3
11 a 56000 L b 56 hours
12 a 20 π m 3 b 300 π cm 3 c 144 π mm 3 d 245 π m 3
13 Answers may vary, an example is r = 5 cm and h = 1.27 cm.
14 x = πh
15 a 14.28 cm 3 b 98.17 mm 3 c 1119.52 cm 3
d 8.90 m 3 e 800 m 3 f 10036.67 cm 3
Exercise 3J
1 a F b D c A
d E e B f C
2 a 120 s b 3 min c 2 h
d 240 min e 72 h f 2 days
g 5 weeks h 280 days
3 a 6 h 30 min b 10 h 45 min
c 16 h 20 min d 4 h 30 min
4 a 180 min b 630 s c 4 min
d 1.5 h e 144 h f 3 days
g 168 h h 1440 min i 4 h
j 2 weeks k 20160 min l 86400 s
5 a 2 h 30 min b 3 h 15 min
c 1 h 45 min
d 4 h 12 min
e 2 h 36 min
f 3 h 12 min 36 s
g 2 h 22 min 48 s
h 7 h 44 min 24 s
i 6 h 1 min 48 s
6 a 1330 h b 2015 h c 1023 h
d 2359 h e 6:30 a.m. f 1 p.m.
g 2:29 p.m. h 7:38 p.m. i 11:51 p.m.
7 a 2 p.m. b 5 a.m.
c 1200 hours d 1800 hours
8 a 2 h 50 min b 6 h 20 min c 2 h 44 min
d 8 h 50 min e 8 h 19 min f 10 h 49 min
9 a 11 a.m. b 12 p.m. c 8 p.m. d 7:30 p.m.
e 7 a.m. f 5 a.m. g 1 a.m. h 10 a.m.
10 a 5:30 a.m. b 7:30 a.m. c 6:30 a.m. d 1:30 p.m.
e 2:30 p.m. f 2:30 a.m. g 3 p.m. h 5:30 p.m.
11 a 5 h b 2.5 h c 8 h d 6 h e 7 h
12 56 million years
13 17 min 28 s
14 7 h 28 min
15 23 h 15 min
16 a 33c b 143c or $1.43
17 a $900 b $90 c $1.50 d 2.5c
18 6:30 a.m.
19 a 8 a.m. 29 March
b 10 p.m. 28 March
c 3 a.m. 29 March
20 3 a.m. 21 April
21 11:30 p.m. 25 October
2252.14 weeks
23 a 3600 b 1440 c 3600 d 1440
24 Friday
25 a You have to turn your clock back.
b You have to turn your clock forward.
c You adjust the date back one day.
26 Students’ reports will vary.
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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