Surface Area and Volume


 Blanche Pitts
 2 years ago
 Views:
Transcription
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
4 Geometry: Shapes. 4.1 Circumference and area of a circle. FM Functional Maths AU (AO2) Assessing Understanding PS (AO3) Problem Solving HOMEWORK 4A
Geometry: Shpes. Circumference nd re of circle HOMEWORK D C 3 5 6 7 8 9 0 3 U Find the circumference of ech of the following circles, round off your nswers to dp. Dimeter 3 cm Rdius c Rdius 8 m d Dimeter
More informationLet us recall some facts you have learnt in previous grades under the topic Area.
6 Are By studying this lesson you will be ble to find the res of sectors of circles, solve problems relted to the res of compound plne figures contining sectors of circles. Ares of plne figures Let us
More information11.1 Kick off with CAS Clculting res with CAS We cn use CAS to define formuls which llow us to quickly nd efficiently clculte the res of different shp
FS O PA G E PR O 11 O R R EC TE D Geometry: similrity nd mensurtion 11.1 Kick off with CAS U N C 11.2 Properties of ngles, tringles nd polygons 11.3 Are nd perimeter I 11.4 Are nd perimeter II 11.5 Gret
More information10 AREA AND VOLUME 1. Before you start. Objectives
10 AREA AND VOLUME 1 The Tower of Pis is circulr bell tower. Construction begn in the 1170s, nd the tower strted lening lmost immeditely becuse of poor foundtion nd loose soil. It is 56.7 metres tll, with
More informationLines and angles. Name. Use a ruler and pencil to draw: a 2 parallel lines. c 2 perpendicular lines. b 2 intersecting lines. Complete the following:
Lines nd s 1 Use ruler nd pencil to drw: 2 prllel lines 2 intersecting lines c 2 perpendiculr lines 2 Complete the following: drw in the digonls on this shpe mrk the interior s on this shpe c mrk equl
More informationPythagoras theorem and trigonometry (2)
HPTR 10 Pythgors theorem nd trigonometry (2) 31 HPTR Liner equtions In hpter 19, Pythgors theorem nd trigonometry were used to find the lengths of sides nd the sizes of ngles in rightngled tringles. These
More informationEnd of term: TEST A. Year 4. Name Class Date. Complete the missing numbers in the sequences below.
End of term: TEST A You will need penil nd ruler. Yer Nme Clss Dte Complete the missing numers in the sequenes elow. 8 30 3 28 2 9 25 00 75 25 2 Put irle round ll of the following shpes whih hve 3 shded.
More information1+(dy/dx) 2 dx. We get dy dx = 3x1/2 = 3 x, = 9x. Hence 1 +
Mth.9 Em Solutions NAME: #.) / #.) / #.) /5 #.) / #5.) / #6.) /5 #7.) / Totl: / Instructions: There re 5 pges nd totl of points on the em. You must show ll necessr work to get credit. You m not use our
More informationPROBLEMS 13  APPLICATIONS OF DERIVATIVES Page 1
PROBLEMS  APPLICATIONS OF DERIVATIVES Pge ( ) Wter seeps out of conicl filter t the constnt rte of 5 cc / sec. When the height of wter level in the cone is 5 cm, find the rte t which the height decreses.
More informationAREA OF A SURFACE OF REVOLUTION
AREA OF A SURFACE OF REVOLUTION h cut r πr h A surfce of revolution is formed when curve is rotted bout line. Such surfce is the lterl boundr of solid of revolution of the tpe discussed in Sections 7.
More informationVolumes of solids of revolution
Volumes of solids of revolution We sometimes need to clculte the volume of solid which cn be obtined by rotting curve bout the xxis. There is strightforwrd technique which enbles this to be done, using
More informationGeometry and Measure. 12am 1am 2am 3am 4am 5am 6am 7am 8am 9am 10am 11am 12pm
Reding Scles There re two things to do when reding scle. 1. Mke sure you know wht ech division on the scle represents. 2. Mke sure you red in the right direction. Mesure Length metres (m), kilometres (km),
More informationNQF Level: 2 US No: 7480
NQF Level: 2 US No: 7480 Assessment Guide Primry Agriculture Rtionl nd irrtionl numers nd numer systems Assessor:.......................................... Workplce / Compny:.................................
More informationUse Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.
Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd
More informationLesson 12.1 Trigonometric Ratios
Lesson 12.1 rigonometric Rtios Nme eriod Dte In Eercises 1 6, give ech nswer s frction in terms of p, q, nd r. 1. sin 2. cos 3. tn 4. sin Q 5. cos Q 6. tn Q p In Eercises 7 12, give ech nswer s deciml
More informationChapter 2 Decimals. (A reminder) In the whole number chapter, we looked at ones, tens, hundreds, thousands and larger numbers. = 1
Chpter 2 Decimls Wht is Deciml? (A reminder) In the whole numer chpter, we looked t ones, tens, hundreds, thousnds nd lrger numers. When single unit is divided into 10 (or 100) its, we hve deciml frctions
More informationExample A rectangular box without lid is to be made from a square cardboard of sides 18 cm by cutting equal squares from each corner and then folding
1 Exmple A rectngulr box without lid is to be mde from squre crdbord of sides 18 cm by cutting equl squres from ech corner nd then folding up the sides. 1 Exmple A rectngulr box without lid is to be mde
More informationReview Problems for the Final of Math 121, Fall 2014
Review Problems for the Finl of Mth, Fll The following is collection of vrious types of smple problems covering sections.,.5, nd.7 6.6 of the text which constitute only prt of the common Mth Finl. Since
More informationCONIC SECTIONS. Chapter 11
CONIC SECTIONS Chpter 11 11.1 Overview 11.1.1 Sections of cone Let l e fied verticl line nd m e nother line intersecting it t fied point V nd inclined to it t n ngle α (Fig. 11.1). Fig. 11.1 Suppose we
More informationDouble Integrals over General Regions
Double Integrls over Generl egions. Let be the region in the plne bounded b the lines, x, nd x. Evlute the double integrl x dx d. Solution. We cn either slice the region verticll or horizontll. ( x x Slicing
More informationRadius of the Earth  Radii Used in Geodesy James R. Clynch February 2006
dius of the Erth  dii Used in Geodesy Jmes. Clynch Februry 006 I. Erth dii Uses There is only one rdius of sphere. The erth is pproximtely sphere nd therefore, for some cses, this pproximtion is dequte.
More informationBinary Representation of Numbers Autar Kaw
Binry Representtion of Numbers Autr Kw After reding this chpter, you should be ble to: 1. convert bse rel number to its binry representtion,. convert binry number to n equivlent bse number. In everydy
More informationFor a solid S for which the cross sections vary, we can approximate the volume using a Riemann sum. A(x i ) x. i=1.
Volumes by Disks nd Wshers Volume of cylinder A cylinder is solid where ll cross sections re the sme. The volume of cylinder is A h where A is the re of cross section nd h is the height of the cylinder.
More informationSect 8.3 Triangles and Hexagons
13 Objective 1: Sect 8.3 Tringles nd Hexgons Understnding nd Clssifying Different Types of Polygons. A Polygon is closed twodimensionl geometric figure consisting of t lest three line segments for its
More informationOperations with Polynomials
38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: Write polynomils in stndrd form nd identify the leding coefficients nd degrees of polynomils Add nd subtrct polynomils Multiply
More informationChapter G  Problems
Chpter G  Problems Blinn College  Physics 2426  Terry Honn Problem G.1 A plne flies horizonlly t speed of 280 mês in position where the erth's mgnetic field hs mgnitude 6.0µ105 T nd is directed t n
More informationRatio and Proportion
Rtio nd Proportion Rtio: The onept of rtio ours frequently nd in wide vriety of wys For exmple: A newspper reports tht the rtio of Repulins to Demorts on ertin Congressionl ommittee is 3 to The student/fulty
More informationThe Quadratic Formula and the Discriminant
99 The Qudrtic Formul nd the Discriminnt Objectives Solve qudrtic equtions by using the Qudrtic Formul. Determine the number of solutions of qudrtic eqution by using the discriminnt. Vocbulry discriminnt
More information, and the number of electrons is 19. e e 1.60 10 C. The negatively charged electrons move in the direction opposite to the conventional current flow.
Prolem 1. f current of 80.0 ma exists in metl wire, how mny electrons flow pst given cross section of the wire in 10.0 min? Sketch the directions of the current nd the electrons motion. Solution: The chrge
More informationLines and Angles. 2. Straight line is a continuous set of points going on forever in both directions:
Lines nd Angles 1. Point shows position. A 2. Stright line is continuous set of points going on forever in oth directions: 3. Ry is line with one endpoint. The other goes on forever. G 4. Line segment
More information15.6. The mean value and the rootmeansquare value of a function. Introduction. Prerequisites. Learning Outcomes. Learning Style
The men vlue nd the rootmensqure vlue of function 5.6 Introduction Currents nd voltges often vry with time nd engineers my wish to know the verge vlue of such current or voltge over some prticulr time
More informationCONNECT: Volume, Surface Area
CONNECT: Volume, Surface Area 1. VOLUMES OF SOLIDS A solid is a threedimensional (3D) object, that is, it has length, width and height. One of these dimensions is sometimes called thickness or depth.
More informationUnit 6: Exponents and Radicals
Eponents nd Rdicls : The Rel Numer Sstem Unit : Eponents nd Rdicls Pure Mth 0 Notes Nturl Numers (N):  counting numers. {,,,,, } Whole Numers (W):  counting numers with 0. {0,,,,,, } Integers (I): 
More information6.2 Volumes of Revolution: The Disk Method
mth ppliction: volumes of revolution, prt ii Volumes of Revolution: The Disk Method One of the simplest pplictions of integrtion (Theorem ) nd the ccumultion process is to determine soclled volumes of
More informationBasic Math Review. Numbers. Important Properties. Absolute Value PROPERTIES OF ADDITION NATURAL NUMBERS {1, 2, 3, 4, 5, }
ƒ Bsic Mth Review Numers NATURAL NUMBERS {1,, 3, 4, 5, } WHOLE NUMBERS {0, 1,, 3, 4, } INTEGERS {, 3,, 1, 0, 1,, } The Numer Line 5 4 3 1 0 1 3 4 5 Negtive integers Positive integers RATIONAL NUMBERS All
More informationMaths Assessment Year 4: Number and Place Value
Nme: Mths Assessment Yer 4: Numer nd Plce Vlue 1. Count in multiples of 6, 7, 9, 25 nd 1 000; find 1 000 more or less thn given numer. 2. Find 1,000 more or less thn given numer. 3. Count ckwrds through
More information9.1 PYTHAGOREAN THEOREM (right triangles)
Simplifying Rdicls: ) 1 b) 60 c) 11 d) 3 e) 7 Solve: ) x 4 9 b) 16 80 c) 9 16 9.1 PYTHAGOREAN THEOREM (right tringles) c If tringle is right tringle then b, b re the legs * c is clled the hypotenuse (side
More informationCHAPTER 9: Moments of Inertia
HPTER 9: Moments of nerti! Moment of nerti of res! Second Moment, or Moment of nerti, of n re! Prllelis Theorem! Rdius of Grtion of n re! Determintion of the Moment of nerti of n re ntegrtion! Moments
More informationLesson 10. Parametric Curves
Return to List of Lessons Lesson 10. Prmetric Curves (A) Prmetric Curves If curve fils the Verticl Line Test, it cn t be expressed by function. In this cse you will encounter problem if you try to find
More informationv T R x m Version PREVIEW Practice 7 carroll (11108) 1
Version PEVIEW Prctice 7 crroll (08) his printout should he 5 questions. Multiplechoice questions y continue on the next colun or pge find ll choices before nswering. Atwood Mchine 05 00 0.0 points A
More informationCUBICFOOT VOLUME OF A LOG
CUBICFOOT VOLUME OF A LOG Wys to clculte cuic foot volume ) xylometer: tu of wter sumerge tree or log in wter nd find volume of wter displced. ) grphic: exmple: log length = 4 feet, ech section feet in
More informationAnswer, Key Homework 8 David McIntyre 1
Answer, Key Homework 8 Dvid McIntyre 1 This printout should hve 17 questions, check tht it is complete. Multiplechoice questions my continue on the net column or pge: find ll choices before mking your
More informationCHAPTER 29 VOLUMES AND SURFACE AREAS OF COMMON SOLIDS
CHAPTER 9 VOLUMES AND SURFACE AREAS OF COMMON EXERCISE 14 Page 9 SOLIDS 1. Change a volume of 1 00 000 cm to cubic metres. 1m = 10 cm or 1cm = 10 6m 6 Hence, 1 00 000 cm = 1 00 000 10 6m = 1. m. Change
More information9 CONTINUOUS DISTRIBUTIONS
9 CONTINUOUS DISTIBUTIONS A rndom vrible whose vlue my fll nywhere in rnge of vlues is continuous rndom vrible nd will be ssocited with some continuous distribution. Continuous distributions re to discrete
More informationPlane figure geometry
2 lne figure geometry ontents: E F G H I Turning Mesuring ngles lssifying nd nming ngles omplementry nd supplementry ngles ngles in revolution isecting ngles onstructing 9 ngles to line lne shpes oints
More informationAnswer, Key Homework 4 David McIntyre Mar 25,
Answer, Key Homework 4 Dvid McIntyre 45123 Mr 25, 2004 1 his printout should hve 18 questions. Multiplechoice questions my continue on the next column or pe find ll choices before mkin your selection.
More information5.2. LINE INTEGRALS 265. Let us quickly review the kind of integrals we have studied so far before we introduce a new one.
5.2. LINE INTEGRALS 265 5.2 Line Integrls 5.2.1 Introduction Let us quickly review the kind of integrls we hve studied so fr before we introduce new one. 1. Definite integrl. Given continuous relvlued
More informationAnswer, Key Homework 10 David McIntyre 1
Answer, Key Homework 10 Dvid McIntyre 1 This printout should hve 22 questions, check tht it is complete. Multiplechoice questions my continue on the next column or pge: find ll choices efore mking your
More informationQuadratic Equations  1
Alger Module A60 Qudrtic Equtions  1 Copyright This puliction The Northern Alert Institute of Technology 00. All Rights Reserved. LAST REVISED Novemer, 008 Qudrtic Equtions  1 Sttement of Prerequisite
More informationThe Math Learning Center PO Box 12929, Salem, Oregon 97309 0929 Math Learning Center
Resource Overview Quntile Mesure: Skill or Concept: 1010Q Determine perimeter using concrete models, nonstndrd units, nd stndrd units. (QT M 146) Use models to develop formuls for finding res of tringles,
More information14.2. The Mean Value and the RootMeanSquare Value. Introduction. Prerequisites. Learning Outcomes
he Men Vlue nd the RootMenSqure Vlue 4. Introduction Currents nd voltges often vry with time nd engineers my wish to know the men vlue of such current or voltge over some prticulr time intervl. he men
More informationChapter 9: Quadratic Equations
Chpter 9: Qudrtic Equtions QUADRATIC EQUATIONS DEFINITION + + c = 0,, c re constnts (generlly integers) ROOTS Synonyms: Solutions or Zeros Cn hve 0, 1, or rel roots Consider the grph of qudrtic equtions.
More informationGraphs on Logarithmic and Semilogarithmic Paper
0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl
More informationApplications to Physics and Engineering
Section 7.5 Applictions to Physics nd Engineering Applictions to Physics nd Engineering Work The term work is used in everydy lnguge to men the totl mount of effort required to perform tsk. In physics
More informationVolume of Prisms, Cones, Pyramids & Spheres (H)
Volume of Prisms, Cones, Pyramids & Spheres (H) A collection of 91 Maths GCSE Sample and Specimen questions from AQA, OCR, PearsonEdexcel and WJEC Eduqas. Name: Total Marks: 1. A cylinder is made of
More informationThree squares with sides 3, 4, and 5 units are used to form the right triangle shown. In a right triangle, the sides have special names.
1 The Pythgoren Theorem MAIN IDEA Find length using the Pythgoren Theorem. New Voulry leg hypotenuse Pythgoren Theorem Mth Online glenoe.om Extr Exmples Personl Tutor SelfChek Quiz Three squres with
More informationSquare Roots Teacher Notes
Henri Picciotto Squre Roots Techer Notes This unit is intended to help students develop n understnding of squre roots from visul / geometric point of view, nd lso to develop their numer sense round this
More informationHomework Assignment 1 Solutions
Dept. of Mth. Sci., WPI MA 1034 Anlysis 4 Bogdn Doytchinov, Term D01 Homework Assignment 1 Solutions 1. Find n eqution of sphere tht hs center t the point (5, 3, 6) nd touches the yzplne. Solution. The
More informationMultiplication and Division  Left to Right. Addition and Subtraction  Left to Right.
Order of Opertions r of Opertions Alger P lese Prenthesis  Do ll grouped opertions first. E cuse Eponents  Second M D er Multipliction nd Division  Left to Right. A unt S hniqu Addition nd Sutrction
More informationr 2 F ds W = r 1 qe ds = q
Chpter 4 The Electric Potentil 4.1 The Importnt Stuff 4.1.1 Electricl Potentil Energy A chrge q moving in constnt electric field E experiences force F = qe from tht field. Also, s we know from our study
More informationCOMPONENTS: COMBINED LOADING
LECTURE COMPONENTS: COMBINED LOADING Third Edition A. J. Clrk School of Engineering Deprtment of Civil nd Environmentl Engineering 24 Chpter 8.4 by Dr. Ibrhim A. Asskkf SPRING 2003 ENES 220 Mechnics of
More informationBrillouin Zones. Physics 3P41 Chris Wiebe
Brillouin Zones Physics 3P41 Chris Wiebe Direct spce to reciprocl spce * = 2 i j πδ ij Rel (direct) spce Reciprocl spce Note: The rel spce nd reciprocl spce vectors re not necessrily in the sme direction
More information104 Surface Area of Prisms and Cylinders
: Finding Lateral Areas and Surface Areas of Prisms 2. Find the lateral area and surface area of the right rectangular prism. : Finding Lateral Areas and Surface Areas of Right Cylinders 3. Find the lateral
More informationMathematics Higher Level
Mthemtics Higher Level Higher Mthemtics Exmintion Section : The Exmintion Mthemtics Higher Level. Structure of the exmintion pper The Higher Mthemtics Exmintion is divided into two ppers s detiled below:
More informationIn Problems #1  #4, find the surface area and volume of each prism.
Geometry Unit Seven: Surface Area & Volume, Practice In Problems #1  #4, find the surface area and volume of each prism. 1. CUBE. RECTANGULAR PRISM 9 cm 5 mm 11 mm mm 9 cm 9 cm. TRIANGULAR PRISM 4. TRIANGULAR
More informationMath 135 Circles and Completing the Square Examples
Mth 135 Circles nd Completing the Squre Exmples A perfect squre is number such tht = b 2 for some rel number b. Some exmples of perfect squres re 4 = 2 2, 16 = 4 2, 169 = 13 2. We wish to hve method for
More informationSection 2.3. Motion Along a Curve. The Calculus of Functions of Several Variables
The Clculus of Functions of Severl Vribles Section 2.3 Motion Along Curve Velocity ccelertion Consider prticle moving in spce so tht its position t time t is given by x(t. We think of x(t s moving long
More informationALPERTON COMMUNITY SCHOOL MATHS FACULTY ACHIEVING GRADE A/A* EXAM PRACTICE BY TOPIC
ALPERTON COMMUNITY SCHOOL MATHS FACULTY ACHIEVING GRADE A/A* EXAM PRACTICE BY TOPIC WEEK Calculator paper Each set of questions is followed by solutions so you can check & mark your own work CONTENTS TOPIC
More informationLecture 15  Curve Fitting Techniques
Lecture 15  Curve Fitting Techniques Topics curve fitting motivtion liner regression Curve fitting  motivtion For root finding, we used given function to identify where it crossed zero where does fx
More informationSection 54 Trigonometric Functions
5 Trigonometric Functions Section 5 Trigonometric Functions Definition of the Trigonometric Functions Clcultor Evlution of Trigonometric Functions Definition of the Trigonometric Functions Alternte Form
More informationTheory of Forces. Forces and Motion
his eek extbook  Red Chpter 4, 5 Competent roblem Solver  Chpter 4 relb Computer Quiz ht s on the next Quiz? Check out smple quiz on web by hurs. ht you missed on first quiz Kinemtics  Everything
More informationThe Calculus of Variations: An Introduction. By Kolo Sunday Goshi
The Clculus of Vritions: An Introduction By Kolo Sundy Goshi Some Greek Mythology Queen Dido of Tyre Fled Tyre fter the deth of her husbnd Arrived t wht is present dy Liby Irbs (King of Liby) offer Tell
More information9.3. The Scalar Product. Introduction. Prerequisites. Learning Outcomes
The Sclr Product 9.3 Introduction There re two kinds of multipliction involving vectors. The first is known s the sclr product or dot product. This is soclled becuse when the sclr product of two vectors
More informationReview guide for the final exam in Math 233
Review guide for the finl exm in Mth 33 1 Bsic mteril. This review includes the reminder of the mteril for mth 33. The finl exm will be cumultive exm with mny of the problems coming from the mteril covered
More informationP.3 Polynomials and Factoring. P.3 an 1. Polynomial STUDY TIP. Example 1 Writing Polynomials in Standard Form. What you should learn
33337_0P03.qp 2/27/06 24 9:3 AM Chpter P Pge 24 Prerequisites P.3 Polynomils nd Fctoring Wht you should lern Polynomils An lgeric epression is collection of vriles nd rel numers. The most common type of
More informationThe remaining two sides of the right triangle are called the legs of the right triangle.
10 MODULE 6. RADICAL EXPRESSIONS 6 Pythgoren Theorem The Pythgoren Theorem An ngle tht mesures 90 degrees is lled right ngle. If one of the ngles of tringle is right ngle, then the tringle is lled right
More information9 Area, Perimeter and Volume
9 Area, Perimeter and Volume 9.1 2D Shapes The following table gives the names of some 2D shapes. In this section we will consider the properties of some of these shapes. Rectangle All angles are right
More informationTriangles, Altitudes, and Area Instructor: Natalya St. Clair
Tringle, nd ltitudes erkeley Mth ircles 015 Lecture Notes Tringles, ltitudes, nd re Instructor: Ntly St. lir *Note: This M session is inspired from vriety of sources, including wesomemth, reteem Mth Zoom,
More information16 Circles and Cylinders
16 Circles and Cylinders 16.1 Introduction to Circles In this section we consider the circle, looking at drawing circles and at the lines that split circles into different parts. A chord joins any two
More informationPicture Match Words. Strobe pictures. Stopping distance. Following. Safety
Tuesdy: Picture Mtch + Spelling Pyrmid Homework [the hndout for it is two pges down] Mterils: 1 bord + 1 set of words per 2 students (totl: 12 of ech) Routine: () once the Pictionry is completed; pirs
More informationD e c i m a l s DECIMALS.
D e i m l s DECIMALS www.mthletis.om.u Deimls DECIMALS A deiml numer is sed on ple vlue. 214.84 hs 2 hundreds, 1 ten, 4 units, 8 tenths nd 4 hundredths. Sometimes different 'levels' of ple vlue re needed
More informationMath Bowl 2009 Written Test Solutions. 2 8i
Mth owl 009 Writte Test Solutios i? i i i i i ( i)( i ( i )( i ) ) 8i i i (i ) 9i 8 9i 9 i How my pirs of turl umers ( m, ) stisfy the equtio? m We hve to hve m d d, the m ; d, the 0 m m Tryig these umers,
More informationMENSURATION. Definition
MENSURATION Definition 1. Mensuration : It is a branch of mathematics which deals with the lengths of lines, areas of surfaces and volumes of solids. 2. Plane Mensuration : It deals with the sides, perimeters
More informationJohn L. Lehet
New! ndroid pp! ST Mthemtics Review Geometry John L. Lehet jehet@mthmverick.com www.mthmverick.com ST Mth Diy Question ndroid pp  new question ech dy  rchive of over 200 questions  different eves nd
More informationWorksheet 24: Optimization
Worksheet 4: Optimiztion Russell Buehler b.r@berkeley.edu 1. Let P 100I I +I+4. For wht vlues of I is P mximum? P 100I I + I + 4 Tking the derivtive, www.xkcd.com P (I + I + 4)(100) 100I(I + 1) (I + I
More informationQuadrilaterals Here are some examples using quadrilaterals
Qudrilterls Here re some exmples using qudrilterls Exmple 30: igonls of rhomus rhomus hs sides length nd one digonl length, wht is the length of the other digonl? 4  Exmple 31: igonls of prllelogrm Given
More informationDyffryn School Ysgol Y Dyffryn Mathematics Faculty
Dyffryn School Ysgol Y Dyffryn Mathematics Faculty Formulae and Facts Booklet Higher Tier Number Facts Sum This means add. Difference This means take away. Product This means multiply. Share This means
More informationPROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY
MAT 0630 INTERNET RESOURCES, REVIEW OF CONCEPTS AND COMMON MISTAKES PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY Contents 1. ACT Compss Prctice Tests 1 2. Common Mistkes 2 3. Distributive
More informationThe formulae for calculating the areas of quadrilaterals, circles and triangles should already be known : Area = 1 2 D x d CIRCLE.
Revision  Areas Chapter 8 Volumes The formulae for calculating the areas of quadrilaterals, circles and triangles should already be known : SQUARE RECTANGE RHOMBUS KITE B dd d D D Area = 2 Area = x B
More informationFormal Languages and Automata Exam
Forml Lnguges nd Automt Exm Fculty of Computers & Informtion Deprtment: Computer Science Grde: Third Course code: CSC 34 Totl Mrk: 8 Dte: 23//2 Time: 3 hours Answer the following questions: ) Consider
More informationTwo special Righttriangles 1. The
Mth Right Tringle Trigonometry Hndout B (length of )  c  (length of side ) (Length of side to ) Pythgoren s Theorem: for tringles with right ngle ( side + side = ) + = c Two specil Righttringles. The
More information5.6 POSITIVE INTEGRAL EXPONENTS
54 (5 ) Chpter 5 Polynoils nd Eponents 5.6 POSITIVE INTEGRAL EXPONENTS In this section The product rule for positive integrl eponents ws presented in Section 5., nd the quotient rule ws presented in Section
More informationAPPLICATION OF INTEGRALS
APPLICATION OF INTEGRALS 59 Chpter 8 APPLICATION OF INTEGRALS One should study Mthemtics ecuse it is only through Mthemtics tht nture cn e conceived in hrmonious form. BIRKHOFF 8. Introduction In geometry,
More information11. PYTHAGORAS THEOREM
11. PYTHAGORAS THEOREM 111 Along the Nile 2 112 Proofs of Pythgors theorem 3 113 Finding sides nd ngles 5 114 Semiirles 7 115 Surds 8 116 Chlking hndll ourt 9 117 Pythgors prolems 10 118 Designing
More informationSURFACE AREAS AND VOLUMES
CHAPTER 1 SURFACE AREAS AND VOLUMES (A) Main Concepts and Results Cuboid whose length l, breadth b and height h (a) Volume of cuboid lbh (b) Total surface area of cuboid 2 ( lb + bh + hl ) (c) Lateral
More informationYour Thoughts. Does the moment of inertia play a part in determining the amount of time it takes an object to get to the bottom of an incline.
Your Thoughts Suppose bll rolls down rmp with coefficient of friction just big enough to keep the bll from slipping. An identicl bll rolls down n identicl rmp with coefficient of friction of. Do both blls
More informationSolving Linear Equations  Formulas
1. Solving Liner Equtions  Formuls Ojective: Solve liner formuls for given vrile. Solving formuls is much like solving generl liner equtions. The only difference is we will hve severl vriles in the prolem
More informationAPPLICATION OF INTEGRALS
Chpter 8 APPLICATION OF INTEGRALS 8.1 Overview This chpter dels with specific ppliction of integrls to find the re under simple curves, re etween lines nd rcs of circles, prols nd ellipses, nd finding
More information