Surface Area and Volume


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1 Surfce Are nd Volume Student Book  Series J Mthletics Instnt Workooks Copyright
2 Surfce re nd volume Student Book  Series J Contents Topics Topic  Surfce re of right prism Topic 2  Surfce re of right cylinder Topic 3  Volume of right prism Topic 4  Volume of right cylinder Topic 5  Volume of pyrmid Topic 6  Volume of right cone Topic 7  Volume of sphere Topic 8  Applictions of re nd volume Dte completed Prctice Tests Topic  Topic test A Topic 2  Topic test B Author of The Topics nd Topic Tests: AS Klr Surfce re nd volume Mthletics Instnt Workooks Series J Copyright 3P Lerning
3 CHAPTER 2 Surfce Surfce Are re nd nd Volume volume Topic : Surfce re of right prism UNIT : Surfce re of right prism QUESTION Find the surfce re of ech cue. 8 m 8 m 9 5 m 8 m 9 5 m 9 5 m QUESTION 2 Find the surfce re of ech rectngulr prism. 9 cm 0 cm 8 3 cm 6 cm 0 4 cm 25 8 cm QUESTION 3 Find the surfce re of ech tringulr prism. 8 cm 2 cm 25 cm 0 cm 7 cm 5 cm 8 cm 32 8 cm QUESTION 4 Find the surfce re of ech shpe. 43 m 38 m 7 4 cm 38 5 cm 95 m 2 m Chpter 2: Surfce Are nd Volume 07 Surfce re nd volume Mthletics Instnt Workooks Series J Copyright 3P Lerning
4 Surfce Are re nd nd Volume volume Topic 2: Surfce re of UNIT right 2: Surfce cylinder re of right cylinder QUESTION For ech cylinder, find the following correct to two deciml plces. i the re of circulr se ii the re of the curved surfce 20 cm 36 cm 8 cm 5 cm QUESTION 2 Find the curved surfce re of ech cylinder in terms of π. 32 cm 3 8 cm 9 3 cm 4 cm QUESTION 3 For ech cylinder, find the following correct to three significnt figures. i the comined re of the two circulr ends ii the re of the curved surfce iii the totl surfce re 4 8 cm 6 m 9 5 cm 0 8 cm QUESTION 4 Find the totl surfce re of the outside of pipe 20 m long with n outer rdius 0 75 m ( pipe does not hve ny ends). Give your nswer correct to one deciml plce. 08 EXCEL ESSENTIAL SKILLS: YEAR 9 MATHEMATICS REVISION AND EXAM WORKBOOK Surfce re nd volume Mthletics Instnt Workooks Series J Copyright 3P Lerning 2
5 Surfce Are nd Volume Surfce re nd volume Topic 3: Volume of right prism UNIT 3: Volume of right prism QUESTION Find the volume of ech cue. 6 m 6 m 7 6 m 6 m 7 6 m 7 6 m QUESTION 2 Find the volume of ech rectngulr prism. 9 6 cm 0 cm 9 3 cm 5 cm 8 8 cm 0 2 cm QUESTION 3 Find the volume of ech tringulr prism. 8 cm 2 cm 32 cm 8 m 4 m 5 m QUESTION 4 Find the volume of ech prism, given the re of the shded fce. A = 78 m 2 23 m A = 60 m 2 48 m Chpter 2: Surfce Are nd Volume 09 Surfce re nd volume Mthletics Instnt Workooks Series J Copyright 3P Lerning 3
6 Surfce Surfce Are re nd nd Volume volume Topic 4: Volume of right UNIT cylinder 4: Volume of right cylinder QUESTION Find the volume of ech cylinder correct to two significnt figures. rdius 6 cm nd height 20 cm rdius 9 6 cm nd height 8 cm c rdius 20 8 cm nd height 30 4 cm d rdius 4 6 m nd height 5 6 m QUESTION 2 Find the volume of ech correct to two deciml plces. 4 6 cm 6 9 cm 9 2 cm 8 4 cm QUESTION 3 Find the volume in cuic centimetres correct to one deciml plce of soft drink cn with height 5 mm nd rdius 30 mm. QUESTION 4 5 cm Which of the following cylinders hs the lrger volume? 30 cm 30 cm 5 cm QUESTION 5 Find the volume of this cylinder in cuic metres correct to three significnt figures. 3 2 m 42 cm 0 EXCEL ESSENTIAL SKILLS: YEAR 9 MATHEMATICS REVISION AND EXAM WORKBOOK Surfce re nd volume Mthletics Instnt Workooks Series J Copyright 3P Lerning 4
7 Surfce Are nd Volume Surfce re nd volume Topic 5: Volume of pyrmid UNIT 5: Volume of pyrmid QUESTION 9 8 cm Clculte the volume of the following squre pyrmids correct to one deciml plce. P 2 5 cm A M B BC = 6 4 cm DC = 6 4 cm PM = 8 2 cm D C QUESTION 2 Clculte the volume of the following rectngulr pyrmids correct to two deciml plces. 5 m 8 7 cm 2 m 9 5 cm 3 4 m 8 9 cm QUESTION 3 Are of the se 4 8 m 2 Clculte the volume of the following pyrmids correct to one deciml plce. perpendiculr height 2 m A P BC = 20 cm AE = 8 3 cm PD = 8 cm B E D C QUESTION 4 The re of the se of n octgonl pyrmid is 225 cm 2 nd its height is 6 4 cm. Find its volume. Chpter 2: Surfce Are nd Volume Surfce re nd volume Mthletics Instnt Workooks Series J Copyright 3P Lerning 5
8 Surfce Are nd Volume Surfce re nd volume UNIT 6: Volume of right cone Topic 6: Volume of right cone QUESTION Find the volume of the following cones correct to one deciml plce cm 6 8 cm 5 6 cm 5 6 cm QUESTION 2 Find the volume of the following cones correct to two deciml plces. 3 6 cm h 8 5 m 8 cm h 2 4 m QUESTION 3 c A cone hs se rdius of 2 cm nd height of 20 cm. Find its volume. Find the volume of cone of height 8 4 cm nd se dimeter 6 2 cm. Find the volume of cone tht hs slnt height of 7 cm nd se dimeter of 6 cm. QUESTION 4 Find the volume of the solid. 5 cm 2 cm 20 cm 2 EXCEL ESSENTIAL SKILLS: YEAR 9 MATHEMATICS REVISION AND EXAM WORKBOOK Surfce re nd volume Mthletics Instnt Workooks Series J Copyright 3P Lerning 6
9 Surfce Are nd Volume Surfce re nd volume Topic 7: Volume of sphere UNIT 7: Volume of sphere QUESTION Find the volume, correct to one deciml plce, of sphere with the following. rdius 7 cm dimeter 8 cm c rdius 25 mm d dimeter 28 m e dimeter 63 cm f rdius 2 4 km QUESTION 2 Clculte the volume of the following spheres correct to one deciml plce. 6 cm 58 cm QUESTION 3 Clculte the volume of the following hemispheres correct to one deciml plce. 52 cm 24 cm QUESTION 4 26 cm Clculte the volume of the following solids correct to one deciml plce. 42 cm 8 cm 24 cm Chpter 2: Surfce Are nd Volume 3 Surfce re nd volume Mthletics Instnt Workooks Series J Copyright 3P Lerning 7
10 Surfce Are nd Volume Surfce re nd volume Topic 8: Applictions of UNIT re 8: nd Applictions volume of re nd volume QUESTION Complete the following. cm 3 = ml 000 cm 3 = L c m 3 = L QUESTION 2 A pot hs volume of cm 3. How mny litres of wter cn it hold? QUESTION 3 The rdius of the erth is pproximtely 6400 km. Given tht the surfce re of sphere is 4πr 2, Clculte the volume correct to four significnt find the surfce re in squre kilometres. figures. QUESTION 4 A rectngulr roof is 28 m long nd 2 m wide. c Wht volume of wter will fll on the roof if we receive 20 mm of rin? A tnk ctches ll the rin tht flls on the roof. How mny litres of wter will flow into the tnk from 20 mm of rin? The tnk holds litres. How much rin would need to fll to fill the tnk if it is empty nd only ctches rin from the ove roof? A rectngulr swimming pool with uniform depth is 30 metres long, 8 metres wide nd 2 8 metres deep. It is to e tiled. Clculte the following. QUESTION 5 the cost of tiling it t $53 per squre metre its cpcity in litres 4 EXCEL ESSENTIAL SKILLS: YEAR 9 MATHEMATICS REVISION AND EXAM WORKBOOK Surfce re nd volume Mthletics Instnt Workooks Series J Copyright 3P Lerning 8
11 Mths Revision Yr 9 Prt 2.qxd:277_pp99_39.qxd 2/2/08 6:4 PM Pge 5 Surfce re nd volume Topic TOPIC Test TEST Surfce Are nd Volume Time llowed: 5 minutes Totl mrks = 5 Time llowed: 5 minutes Totl mrks = 5 The dimeter nd rdius of circle re relted s A rd = 2 B r = 2d C d = 2r D r d = 2 PART PART A A Mrks 2 The circumference of circle is given y the formul A C = 2π B C = 2πr C C = 2πd D C = 2π r 3 The re of circle is given y the formul A A = π B A = π C A = πr2 D A = πd2 r 2 d 2 4 The volume of cylinder with rdius r nd height h equls A V = π2 rh B V = πrh2 C V = 3 πr2 h D V = 2πrh 5 A semicircle equls A full circle B hlf circle C qurter of circle 6 A qudrnt is A 3 4 of circle B 2 of circle C 3 of circle D 4 7 The shded re in the figure is clled A semicircle B segment C chord D sector 8 How mny squre centimetres re there in one squre metre? A 00 B 000 C d D third of circle of circle D A rectngulr prism is 0 cm long, 8 cm wide nd 4 cm high. Its surfce re is D 640 cm2 A 52 cm2 B 304 cm2 C 320 cm2 0 Give the totl surfce re in cm 2 correct to one deciml plce of closed cylinder with dimensions of rdius 6 cm nd height 5 cm. D cm2 A cm2 B cm2 C 79 7 cm2 A cue hs volume of 729 cm 3. Find the length of ech side of the cue. A 6 cm B 9 cm C 8 cm 2 A cylinder hs height 9 m nd rdius 6 m. Its volume is closest to A 3 m3 B 452 m3 C 2036 m3 D 27 cm D 08 m3 3 The volume of rectngulr pyrmid with se re of 75 cm 2 nd verticl height of 8 cm is D 800 cm3 A 200 cm3 B 400 cm3 C 600 cm3 4 The volume of cone with dimeter 2 cm nd height 8 5 cm is closest to A 320 cm3 B 96 cm3 C 282 cm3 5 The volume of sphere of dimeter 24 cm is closest to A 80 cm3 B 7238 cm3 C cm3 D 3845 cm3 D cm3 Totl mrks Totl chieved mrks for PART A 5 5 Surfce re nd volume Chpter 2: Surfce Are nd Volume Mthletics Instnt Workooks Series J Copyright 3P Lerning 5 9
12 Mths Revision Yr 9 Prt 2.qxd:277_pp99_39.qxd 2/2/08 6:4 PM Pge 6 Surfce re nd volume TOPIC TEST Topic Test Surfce Are nd Volume Time llowed: 5 minutes Totl mrks = 5 Time llowed: 5 minutes Totl mrks = 5 Question For this closed cylinder, find the following correct to two deciml plces. 2 8 cm cm PART B PART B the re of circulr se the re of oth the circulr ses c the re of its curved surfce 6 4 cm cm d the totl surfce re e the volume of this closed cylinder Question 2 A swimming pool hs the shpe of trpezoidl prism s shown m Mrks 22 m 2 2 m m Find the volume of the pool in m 3.. Wht is is the cpcity of the pool in kilolitres? c The mss of kl of wter is is t. t. How mny tonnes of wter re in the pool? d Tom trets this pool with chlorine product to prevent the growth of lge. The recommended dose is is 4 g of chlorine for ech 00 L of wter. How much chlorine must Tom plce in the pool? e Over period of hot wether, the level of the pool dropped y 50 cm, The pool ws originlly full. Wht volume of wter, in litres, evported? Question 3 Find the volume of ech of the following correct to two deciml plces. ii ii ii iii perpendiculr height 8 8 m 8 6 cm cm cm cm se re m cm cm The circumference of the erth t the equtor is is out km. ii Use the formul C = 2πr to find the rdius of the erth correct to the nerest 00 km. ii ii Use this rdius to find the volume of the erth correct to two significnt figures. Write your nswer in scientific nottion. equtor Totl mrks Totl chieved mrks for for PART PART B B Surfce re nd volume 6 EXCEL ESSENTIAL SKILLS: YEAR 9 MATHEMATICS REVISION AND EXAM WORKBOOK Mthletics Instnt Workooks Series J Copyright 3P Lerning 5 5 0
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