3. (i) Volume = 1 372 TSA = 196π cm2
(ii) Volume = 9 (iii) 250
(iv) 3 087
___ 3 π cm3
4. (i) 7 cm (ii) 7.3 m (iii) 15 mm (iv) 2.1 km (v) 10.0 cm
____ 4 π mm3
____ 3 π cm3
__ 2 π m3
, , TSA = 9π m2
, TSA = 75π cm2 , TSA = 1 323
____ 4 π mm2
3. (i) 216 cm3 (ii) 94 cm3 (iii) 44%
4. 125 m3 5. 125 cm 6. (i) 216 cm3 (ii) 6 cm (iii) 216 cm2
5. (i) 19 600 cm2 (ii) Height = 1.8 cm
6. (i) 908.8 cm3 (ii) 5 184 cm3 (iii) 47.6% not occupied
Practice questions 16.2
1. (i) 3 456 cm2 (ii) 1 3824 cm3 (iii) 1 810 cm2 (iv) 7 238 cm3 (v) 48%
2. 118 m3 3. (i) 762 cm3 (ii) 200 cm3 (iii) 79 mm3 (iv) 445 cm3
4. Volume = 206 cm3 283 cm2
, surface area =
5. (i) TSA = 575 cm2 (ii) Volume = 855 cm3
7. (i) 22 400 cm3 (ii) TSA = 8 624 cm2
8. (i) 104 719.74 cm3 (ii)
2. 95.5 cm 3. 113 097 cm3 4. (i) 0.032724 m3 (ii) 0.2 m (iii) 0.5 m2
1. (i) 36π cm3 (ii) 90 spheres
5. 125 cm 6. (i) 1 728 cm3 (ii) 339 cm3 (iii) 1 389 cm3 (iv) 20%
7. 2 spheres 8. (i) 19 200π mm3 (ii) 38 528π mm2 (iii) 24 mm (iv) 2 304π mm2
Revision questions
16A Core skills 1. (i) Volume = 320 m3
, surface area = 308 m2 (ii) Volume = 127 512 mm3
(iii) Volume = 1 047 cm3 surface area = 785 cm2
2. (i) 9 900 cm2 (ii) 16 200 cm2 (iii) 236 250 cm3
,
surface area = 115 480 mm2 ,
(a) 219 911 g; (b) 220 kg Practice questions 16.3
6. (i) TSA = 2 073.5 mm2 (ii) 5881.1 mm3
8. (i) 14.14 cm3 (ii) 339.36 cm3 (iii) 648 cm3 (iv) 308.64 cm3 (v) 52%
7. (i) 1 125π cm3 (ii) 9.45 cm
Unit 17 Managing your money
9. (i) 509.3 cm (ii) 400 cm2 (iii) No, surface areas are not the same; any valid mathematical reason with supporting work accepted
11.173.6 m3 12.(i) 188.5 m3 (ii) 47.1 m3 (iii) 75.1%
10.(i) 905 cm3 (ii) 3 cm
16B Taking it further
1. 512 smaller spheres 2. (i) 6 123 cm3 (ii) 1 220 000 cm3
(to three
3. 12.7 cm 4. (i) 118 cm3 (ii) 141 cm3 (iii) (a) Glass B; (b) 19%
significant figures)
Practice questions 17.1 1. Variables = F, P, i, t, constants = number 1; F = final amount, the final sum of money due, including interest, at the end of the investment or borrowing period; P = principal, the sum of money borrowed or invested over a period of time; i = interest rate, the rate at which interest is paid on a loan or savings; t = time, the length of time for which the money is borrowed or invested
2. €443.06 3. A = €165.38, B = €2 497.86, C= €8 555.31, D = €2 410.93, E = €101.51, F = €1 000 499.88
4. €7 400.25 5. €11 077 6. €1 999.08 7. A = €500, B = 3%, C = €6 700, D = 1.19%, E = €301 764.81, F = 43%
8. He should chose account B, as it pays more interest after one year
5. (i) 166.66π cm3 or 500
(ii) 100π cm2 (iii) 10 cm (iv) No, he is not correct; any valid mathematical reason with supporting work
___ 3 π cm
6. 16 ball bearings 7. (i)
16 000
(ii) 10.84 cm (iii) SA = 1 476.62 cm2 (iv) No, Ben is not correct; any valid mathematical reason with supporting work
_____ 3 π or 5 333.33π cm3
8. HA
9. Graph C; any valid mathematical reason
= 4HB
10.(i) 169x2 (ii) x = 1 cm
11.(i) 162π cm3 (ii) 36π cm3 (iii) 40% (iv) No, she is not correct; any valid
mathematical reason with supporting work
12.€1 643.85 13.€1 101.01
10.€755.26 11.(i) €1 207.82 (ii) Total amount repayable: Fast Cash = €4 992.73, Super Loans = €1 690.24, Best Value Loans = €1680.00; Best Value Loans is the better option as you have to pay the least interest on the loan
Practice questions 17.2
2. (i) € 307.50 (ii) €64.58 (iii) €27.08 (iv) €307.96
4. (i) €1 303.79 (ii) €3 350.81
3. (i) €40 000 (ii) €9 730 (iii) €31 920
5. Gross tax due at 21%: €7 413, €9 303, €8 736, €8 158.50, €8 400, €10 440 Gross tax due at 44%: €5 588, €21 868, €43 296, €19 866, €0, €90 420 Total amount of gross tax due: €13 001, €31 171, €52 032, €28 024.50, €8 400, €100 860
Net tax due: €11 351, €28 471, €48 432, €26 574.50, €7 300, €97 110 Net pay (per year): €36 649, €65 529, €91 568, €57 425.50, €32 700, €151 890
Answer key 385
1. (i) €7 654.00 (ii) €5 954.00 (iii) Net salary (a) per year €34 330; (b) per month €2 860.83; (c) per week €660.19
9. (i) 134 rabbits (ii) 180 rabbits (iii) The population is being compounded monthly and not just doubling each month
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