Measurement 1: Surface Area and Volume

Transcription

1 Mesurement 1: Surfce Are nd Volume Student Book - Series M-1 Mthletics Instnt Workooks Copyright

2 Mesurement 1: Surfce re nd volume Student Book - Series M Contents Topics Topic 1 - The re of prts of circle Topic 2 - Are of n nnulus Topic 3 - Are of n ellipse Topic 4 - Are of composite figures Topic 5 - Simpson s rule Topic 6 - Surfce re of cylinder Topic 7 - Surfce re of sphere Topic 8 - Volume of composite solids Topic 9 - Determining errors in clcultions resulting from errors in mesurement Dte completed Prctice Tests Topic 1 - Topic test A Topic 2 - Topic test B Author of The Topics nd Topic Tests: AS Klr Mthletics Instnt Workooks Series M Copyright 3P Lerning ii

3 Topic 1 - The re of prts of circle QUESTION 1 Clculte the re of the following circles, correct to 1 deciml plce. 21 cm 4 cm QUESTION 2 Find the frction of the circle given in the following digrms. c d QUESTION 3 Find the re, correct to 1 deciml plce. c 9 cm 37 cm 60 d e f m km mm Mthletics Instnt Workooks Series M Copyright 3P Lerning 1

4 Topic 2 - Are of n nnulus QUESTION 1 Find the re of the shded region, correct to 1 deciml plce. 4 cm 8 m 6 cm 14 m QUESTION 2 Find the re of the shded region correct to 2 significnt figures. 2.3 m 9.6 m 2.5 cm 10.6 cm QUESTION 3 A 4 metre wide pth is uilt round circulr pool tht hs dimeter of 9 metres. Find the re of the pth correct to 1 deciml plce. 9 m 4 m QUESTION 4 A clock hs minute hnd tht is long nd n hour hnd tht is 3.5 cm long. In one complete revolution of ech hnd, find the difference in the re they cover. (Answer to the nerest squre centimetre.) 3.5 cm 2 EXCEL HSC GENERAL MATHEMATICS REVISION & EXAM WORKBOOK Mthletics Instnt Workooks Series M Copyright 3P Lerning 2

5 Topic 3 - Are of n ellipse QUESTION 1 Find the re of the following ellipses, correct to 1 deciml plce. c 7 cm 1 12 cm 40 mm 18 mm d e f 57 m 9 km 25 cm 32 m 32 km 12 cm QUESTION 2 The re of n ellipse is 84.8 m 2. If the length of the semi-mjor xis is 6 m, find the length of the semi-minor xis. m 6 m Mthletics Instnt Workooks Series M Copyright 3P Lerning 3

6 Topic 4 - Are of composite figures (1) QUESTION 1 Find the re of the following, correct to the nerest cm 2. 5 cm 10 cm 12 cm 6 cm c d 4.5 cm 8.9 cm 8.4 cm 18.6 cm e 45 cm 1 f 40 cm 31 cm 86 cm 4 cm Mthletics Instnt Workooks Series M Copyright 3P Lerning 4

7 Topic 4 - Are of composite figures (2) QUESTION 1 Find the shded re correct to 1 deciml plce. 50 cm 10 cm 16 cm 26 cm c d 0 12 cm QUESTION 2 The digrm shows rectngle inscried inside circle. 6 cm Find the dimeter of the circle. Find the shded re, to 1 deciml plce. 5 Mthletics Instnt Workooks Series M Copyright 3P Lerning 5

8 38 m 36 m 34 m 30 m 32 m Topic 5 - Simpson s rule (1) QUESTION 1 Use Simpson s rule to pproximte the re of the following irregulr shpes. (Answer to the nerest squre metre.) 16 m 15 m 17 m 20 m 37 m 31 m 21 m 21 m 25 m 25 m c 26 m 13 m 18 m 13 m 2 m QUESTION 2 Use Simpson s rule twice to estimte the re of ABCD to the nerest squre metre. A H D F J I G 20 m 18 m 22 m D E 13 m 9 m A B 16 m E G I 16 m 16 m 16 m C C 12 m J 12 m H 12 m F 12 m B Mthletics Instnt Workooks Series M Copyright 3P Lerning 6

9 Topic 5 - Simpson s rule (2) QUESTION 1 Use Simpson s rule twice to find the re of the irregulr shpes with mesurements given in metres B A F 30 E C 30 D 22 I G H QUESTION 2 Use Simpson s rule twice to pproximte this re. QUESTION 3 42 m 24 m 37 m 26 m 20 m 20 m 20 m 20 m 9 m The digrm shows pddock which includes n re of swmpy ground. The totl re of the pddock including the swmpy ground is 2.5 h. Use Simpson s rule twice to estimte the shded re. Swmpy Ground 130 m 108 m 87 m 85 m 120 m 45 m 45 m 45 m 45 m Wht percentge of the pddock is swmpy ground? Mthletics Instnt Workooks Series M Copyright 3P Lerning 7

10 Topic 6 - Surfce re of cylinder QUESTION 1 Clculte the surfce re of the following closed cylinders correct to 2 significnt figures. All mesurements re in centimetres. 9 c QUESTION 2 Clculte the exterior surfce re of the following cylinders correct to 1 deciml plce. All mesurements re in centimetres c open t top closed open t top nd ottom d 7 e f closed open t top nd ottom open t one end Mthletics Instnt Workooks Series M Copyright 3P Lerning 8

11 Topic 7 - Surfce re of sphere QUESTION 1 Find the surfce re of the following spheres with: (correct to the nerest cm 2 ) rdius = 9 cm dimeter = 14 cm c rdius = 2 d dimeter = 36 cm e rdius = 9.4 cm f dimeter = 27. QUESTION 2 Clculte the surfce re of the following spheres. Leve your nswer in terms of π. 10 cm 49 cm QUESTION 3 Clculte the surfce re of the following hemispheres correct to one deciml plce. Find the externl surfce re of this Find the totl surfce re of this hemisphere (open t top). closed hemisphere. 14 cm 35 cm QUESTION 4 A sphere hs surfce re of 360 cm 2. Find its rdius correct to 1 deciml plce. Mthletics Instnt Workooks Series M Copyright 3P Lerning 9

12 6.2 m Topic 8 - Volume of composite solids QUESTION 1 Find the volume of the following solids. 8 m 4 m 6 m 12 m 18.5 m 14 m 22 m 15 m 19 m QUESTION 2 Clculte the volume of the following solids correct to 2 significnt figures. 1.6 m 28 cm 8.4 m 1 30 cm 12.5 m QUESTION 3 Find the volume of the following, correct to 1 deciml plce. 10 cm 16 cm (dimeter of hole = 6 cm) 12 cm 32 cm 10 cm Mthletics Instnt Workooks Series M Copyright 3P Lerning 10

13 Topic 9 - Determining errors in clcultions resulting from errors in mesurement QUESTION 1 Find the re of circle, to 1 deciml plce, with rdius: i 6.2 cm ii 6.3 cm If circle of rdius 6.2 cm hd its rdius incorrectly written down s 6.3 cm wht would e the difference in re? c Wht is the difference s percentge of the ctul re? QUESTION 2 A rectngulr gte ws mesured. Correct to one deciml plce, it ws found to e 4.6 m long nd 1.3 m high. Wht is the re of the gte? c d Between wht two mesurements is the length of the gte? Between wht two mesurements is the width of the gte? Wht is the minimum possile re of the gte? e Wht is the mximum possile re of the gte? f Wht is the difference etween the mximum re nd minimum re? g Express this difference s percentge of the re in. QUESTION 3 Ari mesured cue nd found it hd sides of length 1.2 m. Tht mens the volume of the cue is m 3 he concluded. Comment riefly on the ccurcy of his conclusion, using clcultions to justify your nswer. 11 Mthletics Instnt Workooks Series M Copyright 3P Lerning 11

14 Topic Test PART A Instructions 15 multiple-choice questions Ech question is worth 1 mrk Fill in only ONE CIRCLE Clcultors my e used Time llowed: 20 minutes Totl mrks = 15 1 The re of the semi-circle to the nerest cm 2 is: 14 cm A 77 cm 2 B 154 cm 2 C 30 2 D 616 cm 2 2 The digrm shows sector of circle of rdius 3 m. The re of the sector is closest to: 3 m 40 3 m A 2.1 m 2 B 3.1 m 2 C 4.5 m 2 D 12.6 m 2 3 The surfce re of sphere of rdius 6 cm is closest to: A 151 cm 2 B 452 cm 2 C 905 cm 2 D 2714 cm 2 4 The re of the qudrnt is 78.5 cm 2. To the nerest centimetre, the rdius is: A 4 cm B 5 cm C 7 cm D 10 cm 5 A sector of circle hs rdius 1. The re of this sector is 226 cm 2. The size of the ngle t the centre of the sector, to the nerest degree, is: A 60 B 70 C 80 D The digrm shows cylinder open t oth ends. Its outer surfce re is closest to: A 94 cm 2 B 18 2 C 22 2 D 377 cm 2 12 cm 5 cm 7 The digrm shows rectngle nd semi-circle. The re is closest to: A 114 cm 2 B 153 cm 2 C 209 cm 2 D 322 cm 2 12 cm Mthletics Instnt Workooks Series M Copyright 3P Lerning 12

15 8 The re of the shded nnulus is closest to: 4 cm A 16.9 cm 2 B 37.7 cm 2 C D 164 cm 2 9 The re of the given ellipse is closest to: 1 42 cm A 2375 cm 2 B 756 cm 2 C 1512 cm 2 D 4750 cm 2 10 The shded re is closest to: 16 cm 20 cm A 69 cm 2 B 183 cm 2 C 240 cm 2 D 685 cm 2 11 The volume is closest to: 5 cm 13 cm 3 cm 2 cm A 121 cm 3 B 193 cm 3 C 17 3 D The re of the ellipse is 1021 m 2. The vlue of x is closest to: x m 25 m A 9 B 11 C 13 D m 13 The volume is closest to: 3 m 2 m A 22 m 3 B 23 m 3 C 26 m 3 D 35 m 3 14 The digrm shows rectngle with semi-circle t ech end. The re is closest to: 27 m 33 m A 109 m 2 B 190 m 2 C 194 m 2 D 275 m 2 15 The length of this rectngulr prism ws given s 28.6 cm ut it should e 26.. The volume will e out y: 4 m 5.7 m A 6 m 3 B 10 m 3 C 41 m 3 D 74 m m Mthletics Instnt Workooks Series M Copyright 3P Lerning Totl mrks chieved for PART A 15 13

16 Topic Test PART B Instructions This section consists of 6 questions Show ll necessry working Time llowed: 40 minutes Totl mrks = Find the re correct to 1 deciml plce. 2 mrks ech 5 m 7 cm 50 5 m 7 cm c d 4.6 m 6.3 m 10 cm 1 e 3 cm f 15 cm 25 cm 6 cm 14 EXCEL HSC GENERAL MATHEMATICS REVISION & EXAM WORKBOOK Mthletics Instnt Workooks Series M Copyright 3P Lerning 14

17 17 Find the re, to the nerest m 2. 3 mrks ech 3.6 m 11.2 m 5.6 m 2.4 m 5.8 m 15 m 17 m 18 Find the shded re. Give ech nswer correct to the nerest cm 2. 3 mrks ech 5 cm 7 cm 2.4 cm 9.5 cm 16 cm 16.9 cm 19 Find n pproximtion for the re of these fields, (ll mesurements re in metres), using Simpson s rule: 2 mrks ech once twice Mthletics Instnt Workooks Series M Copyright 3P Lerning 15

18 20 Find the externl surfce re, correct to 2 deciml plces. 2 mrks ech c 21 cm 9 cm 32 cm 23 cm 7 cm Closed Open t top 21 Find the volume: 3 mrks ech 10 m 1 5 m 16 m 18 m 32 cm Totl mrks chieved for PART B 40 Mthletics Instnt Workooks Series M Copyright 3P Lerning 16