10.(i) 175 + 35x (ii) €700 (iii) x = 23 months (iv) 40x = cost (v) Gym B
11.(i) Cost = 2 000 + 125x (iii) €5 750
12.(i) €4 500 (ii) €344 500 (iii) €6.89
13.(ii) InterMaas
(iii) (4, 800) (iv) InterGlen
14.(ii) At 1 month (iii) Verify (1, 5) (iv) Electroquincy
Unit 3 Volume, surface area and net of 3D solids
Practice questions 3.1 1. 105 2. (i) Area = 2 048 m2
,
(ii) Area = 231⋅1 cm2 (iii) Area = 158.5 cm2 (iv) Area = 112⋅5 cm2 (v) Area = 344⋅2 m2 (vi) Area = 1 800 cm2 (vii) Area = 2⋅5 units2 (viii) Area =24⋅6 cm2 (ix) Area = 2 700 cm2 (x) Area = 130 m2
(xi) Area = 74⋅3 cm2 (xii) Area = 87.5 m2
3. (i) 243 m2 (ii) 104⋅94 m2 (iii) 87⋅5 m2 (iv) 600 cm2 (v) 157⋅92 cm2 (vi) 5⋅72 cm2 (vii) 411.92 cm2 (viii) 164⋅39 m2
4. (i) 144 − 36π (ii) 21.5%
5. (ii) 16 cm 6. (i) Length = 25 m (ii) Perimeter = 90 m
7. €240 8. (i) Area of tile = 112⋅5 cm2 0⋅01125 m2
(ii) Area of wall = 1.8 m2 (iii) 18 (iv) Yes
9. Radius = 3 m Radius = 15⋅49 cm
10.(i) Radius = 2 cm (ii) Radius = 6 m (iii) Radius = 9 mm
or
perimeter = 224 m ,
perimeter = 58.5 cm ,
perimeter= 122.8 m ,
perimeter = 192 cm ,
perimeter = 6⋅5 units ,
perimeter = 29⋅9 cm ,
perimeter = 210 cm
, perimeter = 57 m ,
perimeter = 32.6 m
perimeter = 30⋅6 cm ,
perimeter = 57.1 cm ,
perimeter = 45⋅4 cm ,
11.(i) Width = 60 (ii) Length = 25 (iii) Width = 24 (iv) Area = x2
12.(i) 4x + 4 (ii) 12x (iii) x = 0⋅5 m (iv) (a) 1⋅25 m2
13.(i) 44 cm (ii) 100 cm (iii) 2
Practice questions 3.2
2. A, C, F are prisms; B, D, E are not prisms
3. (i) A = 4, B = 1, C = 5, D = 2, E = 3 (ii) A, B and D are prisms; any valid mathematical explanation accepted
Practice questions 3.3
1. (i) 1 860 m3 (ii) 297 cm3 (iii) 7 040 mm3
2. 11 units2 3. (i) 480 m3 (ii) 858 cm3 (iii) 156 m3 (iv) 168 cm3
4. (i) Volume = 567⋅13 m3 (ii) Volume = 300 cm3 (iii) Volume = 357.91 m3 (iv) Volume = 7 600 cm3
5. (i) 18 734 cm3 (ii) 33.6 cm (iii) 4 831.6 cm2
6. (i) F (ii) C (iii) B
7. (i) Surface area = 767⋅5 cm2 (ii) Volume = 1 011⋅5 cm3
8. Height = 5 cm 9. (i) 72 000 cm3 (ii) 120 000 cm3 (iii) 200 minutes
10.(i) 155 m3 (ii) 14 400 litres (iii) No, in 8 hours there will only be 115 200 litres of water in the pool
11.(i) 20 cm2 (ii) 48 cm2 (iii) 21.18 cm
12.(i) 34x2 (ii)
+ 40x + 4 (a) 430 cm2 ; (b) 525 cm3 13.Height in both containers = 25 cm
Practice questions 3.4 1. (i) Volume = 1 206⋅4 cm3
TSA = 703⋅7 cm2
(ii) Volume = 1 696⋅5 cm3 TSA = 791⋅7 cm2
(iii) Volume = 5 674⋅5 cm3 TSA = 1 789 cm2
(iv) Volume = 50⋅3 cm3 TSA = 125⋅7 cm2
,
, , ,
,
surface area = 461⋅58 m2 ,
surface area = 302.46 m2 ,
surface area = 360 cm2 ,
surface area = 1674 cm2
2. (i) 4⋅5 cm3 (ii) 15⋅1 cm2 (iii) 25⋅8 cm2
+ 3x + 2 ; (b) 2 m2
3. A Volume = 77 786 cm3 10 372 cm2
B Volume = 45 738 cm3 4356 cm2
C Volume = 34 861 cm3 4 441 cm2
D Volume = 69 km3 TSA = 94 km2
, CSA =
, TSA = 11 785 cm2 , CSA =
, TSA = 7 128 cm2 , TSA = 5 990 cm2
E Volume = 308 000 cm3 17 600 cm2
5. (i) 1 145⋅69 mm (ii) 1⋅1 m (iii) 11 457 mm3 (iv) 55 coins
6. (i) Any valid mathematical net correctly labelled
7. (i) 502.65 cm3 (ii) 301.6 cm3 (iii) 40%
8. (i) 1 m (ii) 36 cm (iii) 38 cm
9. A = 5⋅5 cm; B = 6⋅2 cm; C = 6⋅6 mm; D = 4⋅1 cm; E = 3 m
10.Minimum height = 10 cm 11.2⋅1 cm 12.(i) 3⋅1 m3 (ii) 2 m
13.(i) 12.6x (x + 1) (ii) Valid substitution
Practice questions 3.5 1. (i) Volume = 3 052⋅1 cm3
, CSA = 1 017⋅4 cm2
(ii) Volume = 179⋅5 cm3 CSA = 153⋅9 cm2
(iii) Volume = 2⋅2 m3 (iv) Volume = 113⋅1 m3 CSA = 113⋅1 m2
2. (i) Volume = 19 396 mm3 CSA = 2 770 mm2 TSA = 4 154 mm2
(vi) Volume = 16⋅3 cm3 ,
(ii) Volume = 90 cm3 TSA = 116 cm2
(iii) Volume = 27 km3 TSA = 51 km2
, ,
, CSA = 8⋅1 m2 ,
(v) Volume = 1 022⋅1 mm3 CSA = 490⋅6 cm2
,
, CSA = 31 cm2 ,
, CSA = 77 cm2 , , CSA = 34 km2
(iv) Volume = 0⋅00006 m3 CSA = 0⋅006 m2 TSA = 0⋅008 m2
3. 972π cm3 4. 0⋅9 m3 5. 54 minutes 6. (i) 518⋅69π mm3 (ii) 213⋅16π mm2
7. (i) 1 630 cm3 (ii) 670 cm2
8. (i) 5 cm (ii) 3 m (iii) 1 m (iv) 18 cm (v) 10⋅9 mm (vi) 27 cm
9. 3 metres 10.(i) 24 429 mm3 (ii) 24 ml (iii) €3⋅33 per ml
Answer key 371 , ,
(ii) 11 250π mm3 (iii) 5 419⋅24 mm2
, CSA = , CSA = 69 km2 , CSA = , TSA = 25 300 cm2
4. Any valid mathematical net correctly labelled
,
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