Module 7 · Answers
Answers & working
Workings shown so you can see where each answer comes from.
Section A — Easy
01
5 faces, 9 edges, 6 vertices
02
120 cm³
V = 6 × 4 × 5.
03
150 cm²
A cube has 6 square faces. SA = 6 × 5² = 150.
04
10 cm
c² = 36 + 64 = 100; c = 10.
05
15 cm
a² = 17² − 8² = 289 − 64 = 225; a = 15.
Section B — Medium
06
V = 120 cm³, SA = 158 cm²
V = 8 × 5 × 3.
SA = 2(8×5 + 8×3 + 5×3) = 2(40 + 24 + 15) = 158.
SA = 2(8×5 + 8×3 + 5×3) = 2(40 + 24 + 15) = 158.
07
6 cm
∛216 = 6.
08
13 cm
c² = 25 + 144 = 169; c = 13.
09
11.4 cm
c² = 49 + 81 = 130; c = √130 ≈ 11.40.
10
5.7 m
h² = 6² − 1.8² = 36 − 3.24 = 32.76; h ≈ 5.72.
11
No — diagonal is 15cm, pencil is 16cm
d² = 12² + 9² = 144 + 81 = 225; d = 15.
Section C — Hard
12
(a) h = 5cm (b) SA = 236 cm²
240 = 8 × 6 × h = 48h → h = 5.
SA = 2(48 + 40 + 30) = 2 × 118 = 236.
SA = 2(48 + 40 + 30) = 2 × 118 = 236.
13
15 cm
d² = 9² + 12² = 81 + 144 = 225; d = 15.
14
40 m shorter
Diagonal: d² = 80² + 60² = 6400 + 3600 = 10 000; d = 100.
Two sides: 80 + 60 = 140. Saving: 140 − 100 = 40.
Two sides: 80 + 60 = 140. Saving: 140 − 100 = 40.
15
(a) h = 12cm (b) Area = 60 cm²
Drop a perpendicular to bisect the base — half-base = 5.
h² = 13² − 5² = 169 − 25 = 144; h = 12.
Area = ½ × 10 × 12 = 60.
h² = 13² − 5² = 169 − 25 = 144; h = 12.
Area = ½ × 10 × 12 = 60.
16
64 cm³
6s² = 96 → s² = 16 → s = 4.
V = 4³ = 64.
V = 4³ = 64.