Surface Area and Volume of Solids

92 Pages·2009·31.55 MB·English

12 FLORIDA
Chapter 12: Surface Area and Volume of Solids
Benchmark Benchmark
12.1 E xploring Geometry Activity: Investigate Solids MA.912.G.7.1 12.5 Exploring Geometry Activity: Investigate the
12.1 Explore Solids MA.912.G.7.2 Volume of a Pyramid MA.912.G.7.5
12.2 Exploring Geometry Activity: Investigate 12.5 Volume of Pyramids and Cones MA.912.G.7.5
Surface Area MA.912.G.7.5 12.5 Spreadsheet Activity: Minimize Surface Area MA.912.G.7.5
12.2 Surface Area of Prisms and Cylinders MA.912.G.7.5 12.6 Surface Area and Volume of Spheres MA.912.G.7.4
12.3 Surface Area of Pyramids and Cones MA.912.G.7.5 12.7 Exploring Geometry Activity: Investigate
12.4 Exploring Geometry Activity: Volume of Right Similar Solids MA.912.G.7.7
and Oblique Prisms MA.912.G.7.1 12.7 Explore Similar Solids MA.912.G.7.6
12.4 Volume of Prisms and Cylinders MA.912.G.7.5
PACING GUIDES* (50-minute classes) Countdown Weeks 23, 24 Calendar Planner®
Full Course
DAY 1 DAY 2 DAY 3 DAY 4 DAY 5
12.1 Geometry Activity 12.1 Lesson 12.2 Geometry Activity 12.3 Lesson 12.3 Lesson
12.1 Lesson 12.2 Lesson Problem Solving
DAY 6 DAY 7 DAY 8 DAY 9 DAY 10
Ready to Go On? 12.4 Lesson 12.5 Spreadsheet Activity 12.5 Lesson Ready to Go On?
12.5 Geometry Activity 12.5 Lesson 12.5 Spreadsheet Activity 12.6 Lesson
12.4 Lesson
DAY 11 DAY 12 DAY 13 DAY 14
12.6 Lesson 12.7 Geometry Activity Problem Solving Chapter Test
12.7 Lesson Chapter Review
Ready to Go On?
Standards Based
DAY 1 DAY 2 DAY 3 DAY 4 DAY 5
12.1 Geometry Activity 12.1 Lesson 12.2 Geometry Activity 12.3 Lesson 12.3 Lesson
12.1 Lesson 12.2 Lesson Problem Solving
DAY 6 DAY 7 DAY 8 DAY 9 DAY 10
Ready to Go On? 12.4 Lesson 12.5 Spreadsheet Activity 12.5 Lesson Ready to Go On?
12.5 Geometry Activity 12.5 Lesson 12.5 Spreadsheet Activity 12.6 Lesson
12.4 Lesson
DAY 11 DAY 12 DAY 13 DAY 14
12.6 Lesson 12.7 Geometry Activity Problem Solving Chapter Test
12.7 Lesson Chapter Review
Ready to Go On?
* Pacing guide for Geometry Honors is found in Planning for Success.
822A
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OOnnggooiinngg AAsssseessssmmeenntt
DIAGNOSE PRESCRIBE
Before Chapter 12
Assess
Diagnose readiness for the chapter. Prescribe intervention.
Prior
Are You Ready? SE Are You Ready? Intervention
Knowledge
Before Every Lesson
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Warm Up TE Skills Review Handbook SE pp. 905–931
Review for Mastery CR
During Every Lesson
Diagnose understanding of lesson concepts. Prescribe intervention.
Guided Practice SE, NTG Reading Strategies BPT
Vocabulary Exercise SE Notetaking Guide
Writing Exercise SE
Questioning Strategies TE
After Every Lesson
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Lesson Quiz TE Review for Mastery CR
Test & Practice Generator, Teacher One Stop @HomeTutor
Formative
Assessment
Before Chapter 12 Testing
Diagnose mastery of concepts in the chapter. Prescribe intervention.
Ready to Go On? SE Ready to Go On? Intervention
Problem Solving Connection SE Review for Mastery CR
Quizzes AR
Chapter Summary and Review SE
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Before Florida Standards Assesment
Diagnose mastery of Florida Standards. Prescribe intervention.
Mastering the Standards SE Focus on Sunshine State
Standards: Intervention
Focus on Sunshine State
Standards: Benchmark Tests
After Chapter 12
Check mastery of chapter concepts. Prescribe intervention.
Summative Multiple-Choice Tests (Levels A, B, C) AR Review for Mastery CR
Assessment Free-Response Tests (Levels A, B, C) AR @HomeTutor
Performance Assessment AR
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KEY: SE = Student Edition TE = Teacher’s Edition CR = Chapter Resources AR = Assessment Resources NTG = Notetaking Guide
Available on CD- or DVD-ROM Available online

822B
GGEE__99778800554477222222000044__CC1122IINN..iinndddd 882222BB 88//77//0099 11::0055::1100 PPMM
12 FLORIDA Resource Options
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Before the Lesson Practice the Lesson
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(cid:129) Editable lesson plans
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assessments. Includes lesson-planning, Complete PowerPoint® presentations for Animated Math, Lesson Quizzes,
test-generation, and puzzle-creation software. every lesson. On Teacher One Stop. Homework Help, and Chapter Project.
822C
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REACHING ALL LEARNERS
All Learners On-Level Learners
Reading and Writing Math ..........................................SE Practice B (cid:74)(cid:71)(cid:56)(cid:69)(cid:64)(cid:74)(cid:63) .........................................................CR
Practice Workbook Problem Solving .............................................................CR
Notetaking Guide Problem Solving Connections ................SE pp. 850, 889
Activity Generator Questioning Strategies ..................................................TE
Pre-AP Resources
Special Needs Students Ready to Go On? Intervention (cid:74)(cid:71)(cid:56)(cid:69)(cid:64)(cid:74)(cid:63)
@HomeTutor
Practice A .......................................................................CR
Animated Geometry
Review for Mastery ......................................................CR
Are You Ready? ...................................................SE p. 822
Inclusion ..............................................................TE p. 845 Advanced Learners
IDEA Works!® Practice C .......................................................................CR
Ready to Go On? Intervention (cid:74)(cid:71)(cid:56)(cid:69)(cid:64)(cid:74)(cid:63) Challenge ........................................................................CR
Animated Geometry Challenge Exercises .....................................................SE
@HomeTutor Problem Solving Connections ................SE pp. 850, 889
Differentiated Instruction .......................TE pp. 844, 875
Math Background Notes ............................................BPT
Developing Learners
Pre-AP Resources
Practice A .......................................................................CR
Are You Ready? Enrichment (cid:74)(cid:71)(cid:56)(cid:69)(cid:64)(cid:74)(cid:63)
Review for Mastery ......................................................CR
Ready To Go On? Enrichment (cid:74)(cid:71)(cid:56)(cid:69)(cid:64)(cid:74)(cid:63)
Are You Ready? ...................................................SE p. 822
Questioning Strategies .................................................TE
Reading and Writing Math ...............................SE p. 890 English Language Learners ELL
Differentiated Instruction ..........................................BPT Are You Ready? Vocabulary .............................SE p. 822
Ready to Go On? Intervention (cid:74)(cid:71)(cid:56)(cid:69)(cid:64)(cid:74)(cid:63) Vocabulary Review ............................................SE p. 892
Animated Geometry English Language Learners ...............................TE p. 828
@HomeTutor Reading and Writing Math ...............................SE p. 890
Multi-Language Visual Glossary
@HomeTutor
Interactive Answers and Solutions Multi-Language Visual Glossary Animated Geometry
Project or print answers to any or all assigned Searchable glossary includes defi nitions in English, Interactive tutorials provide visually engaging
problems. With one click, show the complete Spanish, Haitian Creole, Vietnamese, Chinese, alternative opportunities to learn concepts and
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822D
12
FLORIDA Lesson Practice Level B
L1ES2S.O1N Practice B TThhee tswoloid b iass efos ramree dc obnyg aru peonlty rgeocnta, nsgol iets i,s s ao pito ilsy ha edron. L1ES2S.O1N Practice B continued LE0S.S0ON
For use with pages 824–833 rectangular prism. It has 6 faces, 8 vertices, and 12 edges. For use with pages 824–833
Describe the solid. If it is a polyhedron, fi nd the number of faces, vertices, Determine whether the solid is convex or concave.
and edges. 17. concave 18. convex 19. concave
1. 2. 3.
See above. The solid has a curved surface,
so it is not a polyhedron. The solid has a curved surface,
Use Euler’s Theorem to fi nd the value of n. so it is not a polyhedron.
4. Faces: n4 5. Faces: 1016 6. Faces: 1436
Vertices: 4 Vertices: n Vertices: 24 22. Check sketches;
Edges: 6 Edges: 24 Edges: n Icdirecnutmifyf earnedn csek)e atncdh athreea c.ross section. Then fi nd its perimeter (or r7eÏc}2ta nmg laen wd iwthi dlethn g7t hm ;
LESSON 12.1 S 7k.e tcThri atnhgeu lpaor plyyhraemdirdo n. 8. Pentagonal pyramid 9. Hexagonal prism 20. See below. (cid:19)(cid:0)(cid:67)(cid:77)21. (cid:21)(cid:0)(cid:70)(cid:84) Cscr(cid:28)(cid:28)akihrd ec37eitlu18ccehks.. 45 we5 sffi ;ttft 2;2ht ;A 2 aC. (cid:23)(cid:0)(cid:77)P(cid:28)(cid:23)(cid:0) (cid:77)33.8 m; A(cid:28) 69.3 m2 LESSON 12.1
23. Multiple Choice Assume at least one face of a solid is congruent to at least one
face of another solid. Which two solids can be adjoined by congruent faces to form
ICdheenctkif yy othuer asnosliwd.e Fr iunsdi nthge E nuulemr’bs eTrh oefo fraecme.s, vertices, and edges. ABa ..h eAAxa rthreiecadtnargnougnlu?a lra Bpr yprraismmid a anndd a a r etrcitaanngguullaarr ppyyrraammiidd cw2m0it.2h C shideecsk 3s kcemtc; hPes5; r 1eg5u clmar; p Aen(cid:28)ta g1o5n.5
10. See below. 11. rp1er2cistamn;g 6u,l 1a82r, . tprriiasnmg;u 5la,r 6, 9 McDougalAllrightsreserved IC2n4r oE.sxsDCRcre Seo..rec emcatcAAaisbtsnoi ietcognnrunsiuaiabn t lni2aeTgogr 5 nha upOn –elhr da2iffiasr 7satg mph ,utt re hrruai ieesfnasm ondameutg raroutte nhsphlctdaeot er fasra a nspif cgitgrobrehiuisllsatellm? anos srHhgw ooupolwiyliwnadrsra g cmmpa o yiacminrdnuafb;ybm oi9 enfri aafdmtcahtiecaaosettn saisor einn t .hEexreer?cise 23, which
13. hpyexraamgoidn;a l7 , 7, 14. 15. npoennt-areggounlaalr p rism; ©Holt itsh rionutegrhs etchtreede bvye rat idceiasg oofn tahle p claunbee.. The cross section passes
12 7, 10, 15 Copyright 25. What type of triangle is the shape of the cross sectioenq?uilateral d
26. If the edge length of the cube is 1, what is the length
of the line segment d? Ï}2
27. If the edge length of the cube is 4Ï }2 , what is the
hexagonal prism; 8, 12, 18 perimeter of the cross section? 24
16. Visual Thinking An architect is designing a contemporary offi ce building in the
shape of a pyramid. The building will have eight sides. What is the shape of the base
of the building? octagon
10. regular pyramid; 5, 5, 8
Geometry Geometry
390 Chapter 12 Resource Book Chapter 12 Resource Book 391
L1ES2S.O2N Practice B L1ES2S.O2N Practice B continued LE0S.S0ON
For use with pages 834–841 For use with pages 834–841
LESSON 12.2 SR 1ko.eutncdh ytohuer p aonlsywheedr rtoon t Crweh3oep cc rmkdeescei2nm.teaCd2lh 4 peb iclnyak. ctsehkeset. cnheets.; 4T6h5e6n i nfi. 2nd th3e. suCr1hf0ea cfckte s kaertechae. s; 345.65 8ft ft2 1134.. SatSlpeenruugridmsrr lmffaesaa n hccoigseeeft iAA7hxg ,hrritnhyeet ,caaao aht f oonei ysffds . aa6u zW n.PPinihtrrScsiia h.ss5t Tmme is sh2 eatxAAh nyd edrte1 r esptichua t2thenrafx gnoaozugcfth1l eutae hlra are2 r pr ley perpazigrrs io imslsfemm ntw hg ihesitt ah hzps tr uahai ns arbmiittg asi?shs. e tW8 t2w rir1iniia6ttchne hi gntaeuh .sw2le.a Tisrd uhbtrehaf sahoecef e hix gaa husrte n oaoin tfSse t hine LESSON 12.2
sketches;162 55 in. 60 in.
cm2 15. Surface Area of a Prism A triangular prism with a triangular base has legs with
12 cm lengths of 5 inches, 5 inches, and 6 inches. The height of the prism is 10 inches.
What is the surface area of the prism? 184 in.2
Sketch a net of the right prism. Find the surface area and lateral area of
the prism. Round your answers to two decimal places. 16. Multiple Choice The radius and height of a right cylinder are each multiplied by 2.
Check sketches; 309.21 ft2; 269.21 ft2 What is the change in the surface area of the cylinder? B
4. 5. 6. 5 cm A. The surface area is 2 times the original surface area.
6m 4 cm B. The surface area is 4 times the original surface area.
C. The surface area is 6 times the original surface area.
Check1 0skmetches; 2448m m2; 168 m2 5 ft 12 ft 6 cm 17. DSu. rTfahcee sAurrfeaac eo fa are Ca yisl i8n dtiemre sT hthee r oadriiguisn aaln dsu hrfeaigceh ta oref aa. right cylinder are each
8 ft Check sketches; 228.06 cm2; 150 cm2 18. dRiavdidieuds boyf a2 .C Wylhinatd iesr t hFei nchda tnhgee r aind isuusr foafc ae rairgehaTt hocefy ltnihneewd ce ysr ulwirnfidathce era? asrueraf aisc e} 14 a orfe ath oef original surface area.
Find the surface area and lateral area of the right cylinder using the given 48(cid:58) square feet. The height of the cylinder is 5 feet. 3 ft
radiusr and height h. Round your answers to two decimal places.
7. r5 5 cm; h5 1652 8c.m32 cm2 8. r5 1.1 ft; h5 32.92. 7f2t ft2 9. r5 12 in.; h5 18 in2.261.95 in.2 19. Ca caynldinyd Briocxa l Abosx a obfi rctahnddayy. pTrhees ednita mfoert ae rf roife nthde, ybooux bisu y
471.24 cm2 22.12 ft2 1357.17 in.2 6 inches and the height is 8 inches. What is the minimum
amount of wrapping paper needed to wrap the gift?
MOOTILOR Allrightsreserved In ExRerocuinsde yso 2u0r –an2s2w, eur stoe ttwhoe d feoclimloawl pinlagc eisn. fo20rm7.3a5t iionn.2. CANDY
Solve for x given the surface area S of the right prism or right cylinder. McDougal Wpipaet etrh aDt risa inneaegdee dP ifpoer tTheh ec ofi ngsutrreu catti othne o rfi gah nt eswho dwrisv aew daray.i nage
R10o.unSd5 y o3u20r amn2sw8 mer to two de1ci1m.aSl p5l a2c0e0s f.t2 10.23 ft 12. S5 1000 cm8 2cm11.89 cm Copyright©Holt Tt2hh0ae.t opfiItp hft eehth ehme al iedsnn eiagms tilhgeun.nm gR i tsdoh eut oopn ftdh h1 a y5ovo fefu etarhe tea tl neadsaniwtsdcte haor? snd eti2oa f. m5otw oeftott e odrf et phcaaimvt eiasml opennlaetc oteevsne.trh t he drainage pipe, what is
8m x 21. What is the surface area of the drainage pipe? 70.69 ft2
22. What is the surface area of the drainage pipe, if the diameter of the pipe is one sixth
4 ft x of the length of the pipe? 117.81 ft2
6m
6 ft
x
Geometry Geometry
400 Chapter 12 Resource Book Chapter 12 Resource Book 401
822E
L1ES2S.O3N Practice B L1ES2S.O3N Practice B continued
For use with pages 842–849 For use with pages 842–849
Find the area of each lateral face of the regular pyramid. Round your Sketch the described solid and fi nd its surface area. Round your answer to
answer to two decimal places. two decimal places.
1. 12 m2 2. 48 ft2 3. 18 cm 232.05 cm2 14. A regular pyramid has a slant height of 15. A regular pyramid has a height of 10 inches.
12 inches. Its base is a square with a Its base is an equilateral triangle with a base
6m 12 ft base edge length of 18 inches. 756 in.2 edge length of 12 inches. 252.85 in.2
12 in. 10 in.
8 ft 12 in.
4m 22 cm 18 in. 12 in.
12 in.
Sketch a net of the regular pyramid. Find its surface area and lateral area.
Round your answers to two decimal places.
4. 1C 0hm ec1k8 s9k emtc2h;e5s;. 14 ft 6. 11 cm 16. Aa h reigighht tc oofn 9e hfeaest .a r1a1d7i.u6s9 o fft 23 feet and 17. Aa s rliagnhtt h ceoingeh th oafs 9a mdieatmerest.e r2 o8f2 .1724 mme2ters and
140 m2 3 ft
12m
13 cm 9 ft
9 ft 9 ft Check sketches; 287.68 cm2 9m
7m Check sketches; 588.44 ft2; 214.5 cm2
378.00 ft2
Find the lateral area of the right cone. Round your answer to two
decimal places. 188.5 ft2
7. 157.08 m2 8. 6 ft 9. 304.52 cm2 Fairned r itghhet .s Rurofuancde ayroeuar oafn sthwee sr otloid t.w Toh ed epcyirmamal ipdlsa caeres .regular and the cones
5m 10m 8 ft 6 cm 15 cm Allrightsreserved 18. 14080m m2 1191.398. in.27 i2n .in. 5 in. 20. 124.71 cm26 cm
Fd 1ie0nc.dim thael psluarcfeasc.e5 7a8re.0a5 omf2 the ri1g1h.t cone. R1o4u ftnd you4r4 0a.n67s wft2e1r 2t.o two 1160.06 cm2 HoltMcDougal 8m 8m 6 cm
LESSON 12.3 13. Mul8timple Cho1i5cem The surface area of a regular1 1p yftramid with a square 1b0a scem is 25 cm Copyright© IGEobdnfealr csaGeEeinam xicwtzea iaPeilr,t n hycpEt ril agsaEa cyebmgepasysits pd..2e tP .1oe yTfd–r hgKa2eem3h Gli,ued runfseug saw tethT e P rhtoyehef r bea7Gum 5fri6eolitd a lft tleoi osPe wsty4.e r8Rrian1vmoe gfu ie adnies dnto t fhfyoo iomKgruhmhbr us aaa ffnnutods irwi o sht nehalroes.s c apta ohtse aqtdrwua aioonr he s LESSON 12.3
1536 square meters. The base edge length is 24 meters and the slant height is 21. Approximate the slant height of the Great Pyramid. 611.76 ft
20 meters. What is the height of the pyramid? C
22. Approximate the area of each lateral face of the Great Pyramid. 231,243.64 ft2
A. 8 meters B. 12 meters C. 16 meters D. 20 meters
23. Approximate the surface area of the Great Pyramid. 924,974.57 ft2
Geometry Geometry
410 Chapter 12 Resource Book Chapter 12 Resource Book 411
L1ES2S.O4N PFor rusae wcitht piacgese 85 3B–859 L1ES2S.O4N FPor rusae wcitht piacgese 85 3B–85 9continued LE0S.S0ON
Fc io1nn.dt a5tihnee dvo ilnu mt4hee osfo3 ltihd1ue.n2 5i0st soculibdi c2by2 d.e1t3e2r0m c3uinbii2cn gun hi2tosw27 many35 unit3 c.ub143e6s3 caurb3ei c2 units107 25 LESSON 12.4 LESSON 12.4 Sd 11e34kc..e itmcA1MAh0a. ur li et l2nchpt4citelpah an leedcgs e euClosslhan.crogr ip,ic br8eies imdHnc oswhwoeits lmh iwd aaB i nadh.ye ne ,3i2d ga2 hinfint d cno h4df ci 3niu tfcbsehe eesvts ,oc talaunll mfi?1 te5 Cc. .o RmCAop. rul ie4gnt0hed lt y yc yionlui anr d baeornx ws twhitahet aris rt aod Dituw.s oo3f 2 04 meters and
4 10 6 width of 6 feet, and length of 9 feet. 162 ft3 a height of 8 meters. 402.12 m3
9
4m
Find the volume of the right prism or right cylinder. Round your answer to 3 ft
two decimal places. 189 in.3 6 ft 8m
4. 96 m3 5. 9 ft
3 in. Find the volume of the solid. The prisms and cylinders are right.
Round your answer to two decimal places.
6m 7 in. 16. 3 mm 48 mm3 17. 2 in. 502.65 in.3
9 in. 4 mm
4m 7 in.
8m 6 mm 5 in.
6. 831.38 cm3 7. 113.1 ft3
3 ft
5 mm
4 ft 4 mm
Use Cavalieri’s Principle to fi nd the volume of the oblique prism or
D8e.sc5r iibne. th8 ec msoli1d2. i n5F. icnmd th9e4 l2e.4n8g tinh. 3x using th9e. gi2v cemn volume V2.2 cm 276.46 cm3 c 1y8li7.n2d me4rm .m 3Rmound you6 rm amnsw3 emrm to1 9t.w625o. 8i nd3. einc.i3mal p2la inc.es. 20. 6 cm 3041 c.m59 cm3 ©HoltMcDougalAllrightsreserved
10. V5 1440 m3 11. V5 3601 7ft 3ft x 12. V5 72(cid:58) cxm3 IPpniill llEaarxrses o ruIcnti sooefr dspe l2ra s1ttoe– rm2 o3of,d peuals raies h . toThmheee ,fp oyilollluaor nws ewiendilg lt obi enc rfseohaartpmee fado tuairso mrne.ignuilaatru re Copyright
8m 2 cm hexagonal prisms with a face width of 2 inches and a height of
12 inches. Round your answers to two decimal places.
8 ft 12 in.
x right rectangular prism; 6 ft right cylinder; 6 cm 21. What is the area of the base of a pillar? 10.39 in.2
15m 22. How much plaster of paris is needed for one pillar? 124.71 in.3
rectangular prism; 12 m 23. Is 480 cubic inches enough plaster of paris for all four pillars?no 2 in.
Geometry Geometry
Chapter 12 Resource Book 421 422 Chapter 12 Resource Book
822F
12
FLORIDA Lesson Practice Level B
L1ES2S.O5N Practice B L1ES2S.O5N Practice B continued LE0S.S0ON
For use with pages 862–871 For use with pages 862–871
Describe the solid. Find its volume. Round your answer to Find the volume of the solid. The prisms, pyramids, and cones are right.
two decimal places. regular square pyramid; 20 in.3 Round your answer to two decimal places.
1. r1i0g0h.t5 c3o cnme;3 2. 4 in. 3. 4 cm 14. 6m 448 m3 15. 7 in. 90.93 in.3
6 cm 4 cm 4 cm 5m 2 in. 5 in.
3 in.
4 cm 5 in. regular triangular pyramid; 10.67 cm3 8m 8m
4. 5. 6. 16. 144 cm3 17. 2 mm 190.87 mm3
8 cm 6 cm
11m 9 in. 5 cm 6 mm
LESSON 12.5 Find othbleiq vuae lcuoen eo;f 4 6x1m.4.69 m3 non-regu7 lianr. square pyr6a mini.d; 126 inr.i3ght cone; 163.49 cm3 18. 6 cm6 9c min. 103.67 in.3 19. 6 m6m mm 6 4m cmm 122.67 cm3 LESSON 12.5
7. V5 64 in.36 in. 8. V5 147(cid:58) cm37 cm 9. V5 56 m37 m 4 cm
x 2 in. 6 in. 3 in. 4 cm
9 cm x 10m
4 in. x 6m 6 cm
8 in.
6 cm
10. Multiple Choice A right cone has a height of 6 feet and a volume of 32(cid:58) cubic feet.
What is its radius? C 20. Height of a Pyramid A right pyramid with a square base has a volume of
16 cubic feet. The height is six times the base edge length. What is the height
A. 2 ft B. 3 ft of the pyramid? 12 ft
C. 4 ft D. 5 ft
6 ft In Exercises 21–23, use the following information.
Concrete To complete a construction job, a contractor needs 78 cubic yards of concrete.
? The contractor has a conical pile of concrete mix that measures 22 feet in diameter and
12 feet high.
Find the volume of the right cone. Round your answer to two 21. How many cubic feet of concrete are available to the contractor? 1520.53 ft3
decimal places.
11. 2035.75 cm3 12. 3681.88 m3 13. 2652.53 ft3 22. How many cubic yards of concrete are available to the contractor? 56.32 yd3
13m 268 23. Does the contractor have enough concrete to fi nish the job? no
328
18 cm 22 ft
608
Geometry Geometry
432 Chapter 12 Resource Book Chapter 12 Resource Book 433
L1ES2S.O6N PFor rusae wcitht piacgese 87 2B–879 L1ES2S.O6N FPor rusae wcitht piacgese 87 2B–87 9continued
Find the surface area of the sphere. Round your answer to two Find the surface area and the volume of the solid. The cylinders and cones
decimal places. are right. Round your answer to two decimal places. Write verbal models
1. 201.06 cm2 2. 28.27 in.2 3. 61145.m75 m2 t 1o6 e.xplain the formulas you us1e7.. 18. 6 ft
4 cm 32 in. 6 cm
3 in. 17 ft
4 cm
See below. See below.9 in. See below.
4. Multiple Choice What is the approximate radius of a sphere with a surface area of Complete the table below. Leave your answers in terms of π.
40(cid:58) square feet? B
A. 2 ft B. 3.16 ft C. 6.32 ft D. 10 ft Radius of sphere Circumference of Surface area of Volume of sphere
great circle sphere
In Exercises 5–7, use the sphere below. The center of the sphere is C and 19. 12 mm 24p mm 576p mm2 2304p mm3
its circumference is 7(cid:58) centimeters.
56.. FFiinndd tthhee rdaidamiuest oerf othfe t hsep hseprhee. re }72. c7m cm C 2201.. 4}72 ifnt. 87πp ifnt. 6449pπ ifnt.22 }2}3356463pp ifnt.33
7. Find the surface area of one hemisphere. 22. 6 m 12p m 144p m2 288π m3
Round your answer to two decimal places. 76.97 cm2
8. Great Circle The circumference of a great circle of a sphere is 24.6(cid:58) meters. What is 23. Finding a Diameter The volume of a sphere is 972π cubic centimeters. What is the
LESSON 12.6 F in9d. tthhee s uvrofalucem aere oa fo f1t h4th3ee6 s.s7pp6hh efetr3ree? .1R R0o.ouundn dyo yuor uanrs awnesr wtoe 3twr8 1ot.o 7d etycwdim3oa dl1 ep1lc.aicmesa. l 1p9l0a1c.e17s .m2 211644m.66 m3 IGanreo E lofx fBtdeeairnalc mlssios elAetdes rsi nt2oa f4an t d–bha2oer x6ds p, og hfuo efslrofee ub? rta .h l1Ale 8hs sacfusmo mall eod iwtahmainte gtthe eri n obffao l1lrs.m6 a8ra eitn ipcoahncek.se. dG toiglfh btlayl lsso SSuuppeerr-F-FlylyXL LESSON 12.6
7 ft 92 yd that they touch the lateral sides and the bases of the box.
24. What is the surface area of a golf ball? about 8.87 in.2
25. What is the volume of a golf ball? about 2.48 in.3
26. What is the amount of volume inside the box that is not taken up by the golf balls? about 9.04 in.3
Ftoin tdw toh ed eracdimiuasl opfla tchees .sphere with the given volume V. Round your answer S1u6r.f 4ac9e0 .A09re cam o2f; h 9e0m4i.s7p8h cemre3;; V Soulrufmacee = A Vreoalu 5m eS uorff cayceli nadreear 1of Vcyolliunmdeer o2f hAermeais opfh eornee base 1
12. V5 64 in.3 2.48 in. 13. V5 150(cid:58) cm3 4.83 cm 14. V5 152 m3 3.31 m f1a7c.e 2A5r4e.a4 7o fi nh.e2m; 1is4p1h.3e7re i;n V.3oSluumrfea c5e AVroelau m5e Souf rcfyaclien dareera 2 o fV coylulimndee or f2 h eAmreisap ohfe roene base 1 Sur-
15. Multiple Choice What is the approximate radius of a sphere with a volume of h1e8m.i5s6p6h.e0r1e ;f tV2o; l u1m09e3 =.2 V7 ofltu3mSuer foafc ceo Anere +a V=o Sluumrfaec oef ahreema oisfp choenree 2 Area of base + Surface Area of
128(cid:58) cubic centimeters? B
A. 2.5 cm B. 4.58 cm C. 6.62 cm D. 8 cm
Geometry Geometry
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L1ES2S.O7N Practice B L1ES2S.O7N Practice B continued
For use with pages 880–888 For use with pages 880–888
LESSON 12.7 Ts ce1al.ll ew fhaectthoerr. the pa6ir 8c s omcimmf irliagr;h 2t: 1solids4 icsm similar2. .If s6 oft, de3t eftrmine thsiem ila2r ;f t3:2 S11o.lid AS i=s 2sA0i8m mil2ar to S2o;liS1d = B B5.2 Fmin2d the scale f1a2c.tor of SBolid A 2t;o3 SolidA B. LESSON 12.7
14 cm 7 cm 3 cm 4 ft
S = 63p cm2 S = 28p cm2
not similar 13. 3;4 A 14. 3;2
3. 4 mm 4 mm 4. 2s mimilar; 1:0.6 V = 27 ft3 A B
10 mm 6 mm 5 mm 4 mm 3 m 4.5 m 1.8 m 2.7 m1.2 m V = 64B ft3 V = 54 in.3 V = 16 in.3
5. Mto ua lrtiigphlet cCyhlionidceer Wthahti cish ssiemt iolaf rd tiom tehnes cioynlisn cdoerrr sehsopwonnd?s D 5 in. Solid A is similar to Solid B. Find the surface area and volume of Solid B.
15. 16.
A.r5 2, h5 5 B. r5 3, h5 7 18 mm
9 in. 2 3m
C.r5 10, h5 19 D. r5 15, h5 27 B 8m
A 4m A 12 mm B 10 mm
4m 975p mm2; 4500p mm3
4m
Solid A (shown) is similar to Solid B (not shown) with the given scale about 385.6 m2; about 330.98 m3
factor of A to B. Find the surface area and volume of Solid B. 17. Finding a Ratio Two cubes have volumes of 64 cubic feet and 216 cubic feet.
6. Scale factor of 1:2 7. Scale factor of 1:3 8. Scale factor of 2:3 What is the ratio of the surface area of the smaller cube to the surface area of
the larger cube? 4;9
S5 42p ft2,V5 36 p ft3 S5 96 p m2,V5 96 p m3 S5 75.6 cm2,V5 36 cm3
In Exercises 18–22, use the following information.
A Water Tower As part of a class project, you obtain the responsibility 12 ft
of making a scale model of the water tower in your town. The water
A tower’s diameter is 12 feet and the height is 16 feet. You decide that
A 0w.a5t einr cthow ine ry.our model will correspond to 12 inches of the actual 16 ft
168p ft2; 288p ft3 864p m2; 2592p m3 170.1 cm2; 121.5 cm3 18. What is the scale factor? 1;24
9. Fhains dai snugr fSaucref aarceea A orfe 1a6 πTw sqou saprhee freeest .h Favined a tshcea sleu rffaaccteo ra roefa 1 o:f3 t.h Teh lea rsgmera lslpehr esrpeh. e1re4 4p ft2 19. What is the radius and height of the model?r5 3 in.; h5 8 in.
10. Multiple Choice Two right cylinders are similar. The surface areas are 24π and 20. What is the surface area of the model? 66p in.2
96π. What is the ratio of the volumes of the cylinders? B 21. What is the volume of the actual water tower? of the model? 576p ft3; 72pin.3
A. }14 B. }18 C. }12 D. }23 22. Sthuepirp osuserf yacoeu amreaakse? ao sf etchoenird v soclaulme ems?o d1e l: c1o;n 1g r: u1ent to the fi rst. What is the ratio of
Geometry Geometry
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12
FLORIDA Assessment
CH1AP2TER QFor uusei azfte r 1Lessons 12.1–12.3 CH1AP2TER QFor uusei azfte r 2Lessons 12.4–12.5
1. A polyhedron has 6 vertices and 9 edges. How many faces does the Answers Find the volume of the fi gure. Round your answer to two Answers
polyhedron have? 1. 5 faces decimal places, if needed. 1. 756 in.3
Check sketches; 1.
Sketch a net of the right prism. Find the surface area 2. 632 cm2, 440 cm2 6 in. 2. 1728 cm3
and lateral area of the prism. Round your answers to Check sketches;
two decimal places. 3. 528 in.2, 480 in.2 9 in. 3. 2412.74 ft3
2. 3. 4.1357.17 ft2; 848.23 ft2 14 in. 4. 47,123.89 m3
10 cm Check sketches; 2.
5. 420 ft2, 320 ft2 5. 16 cm3
16 cm 6 cm 8 in. 20 in. 6.1130.97 m2; 816.81 m2 18 cm
8 cm
6 in. 24 cm
4. Find the surface area and 3.
lateral area of the right cylinder.
Round your answer to
two decimal places. 15ft 12ft
9ft 8ft
5. Spykreatmchi da. nFeitn do fi ttsh es urrefgauclea ra r ea 4.
and lateral area. Round your
answers to two decimal places. 16ft 50m
30m
10ft
5.
6. Find the surface area and
the lateral area of the right cone.
3 cm
Round your answer to 24m
two decimal places.
4 cm
4 cm
10m
Geometry Geometry
Chapter 12 Assessment Book 231 232 Chapter 12 Assessment Book
CHAPTER Quiz 3 CHAPTER Chapter Test B
12 12
For use after Lessons 12.6–12.7 For use after Chapter 12
Find the surface area and volume of the sphere. Round your Answers Describe the solid. If it is a polyhedron, fi nd the number of Answers
answers to two decimal places. 1. 804.25 in.2; faces, vertices, and edges. 1. polyhedron; 7 faces,
1. 1. 2. 3.
2144.66 in.3 7 vertices, 12 edges
2. 1134.11 ft2; 2. not a polyhedron
8 in.
3591.36 ft3
2. 3. 2827.43 cm2; Use Euler’s Theorem to fi nd the value of n. 3.polyhedron; 10 faces,
4. Faces: 8 5. Faces: 9 6. Faces: n
14,137.17 cm3 Vertices: 12 Vertices: n Vertices: 16 16 vertices, 24 edges
Edges: n Edges: 21 Edges: 24
9.5ft 4. 480 ft2, 480 ft3 4. 18
5. 9047.79 cm2, Fpiynrda mthide ss uarrefa rceeg aurlaera aanndd tlhaete prarils amresa, coofn tehse, saonldid c. yTlihned ers are 5. 14
3. 80,424.77 cm3 right. Round your answers to two decimal places, if necessary. 6. 10
7. 8.
6. 28:17 10 ft 7. 712 ft2
30 cm 6.8 m 460 ft2
9 ft
14 ft 3.5 m 8. 226.51 m2
Sgiovleidn Asc (aslheo fwacnt)o irs osfim Ai ltaor Bto. FSionldid t hBe ( nsoutr fsahcoew anre) aw Sit ha ntdh e 9. 10. 36 in. 149.54 m2
volumeV of Solid B.
4. Scale factor 1:2 5. Scale factor 1:4 9. 538.08 cm2
S5 120 ft2 S5 180(cid:58) cm2 8 cm 16 cm 27 in. 371.81 cm2
V5 60 ft3 V5 400(cid:58) cm3 11. 7.4 yd 12. 10. 6107.26 in.2
40 m 3817.04 ft2
11. 172.03 yd2
20 m
32 m 12. 2688 m2
Solve for x given the surface area Sof the right solid. Round 1920 m2
6. Two similar spheres have surface areas 784(cid:58) square meters and your answer to the nearest meter.
289(cid:58) square feet. What is the scale factor of the larger sphere to 13. S = 6372 m2 14. S = 325 m2 15. S = 2513.3 m2 13. 50 m
the smaller sphere?
45 m 14. 7 m
x x x 15. 34 m
27 m 4.5 m 16 m
Geometry Geometry
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CH1AP2TER Chapter Test B continued CH1AP2TER Standardized Test B
For use after Chapter 12 For use after Chapter 12
Find the volume of the solid. The pyramids are regular and the Answers Multiple Choice 7. Find the surface area
pt1w6ri.osm dse,c cimonael sp,l aacneds ,c yifl innedceersss aarrey1 .r7i.ght. Round your answers to 1167.. 142372.509 c min3.3 1.A Which fi gure is not a Bpolyhedron? C CAof 41th86e95 66re mmgu22lar BDpyr a22m71i38d64. mmB22 45 m
41 cm 8.9 in. 18. 179.59 km3
24 m
19. 1018.45 m3 C D 8. Find the lateral area 5 in.
18 cm 18 cm 3.7 in. 20. S 5 628.32 m2, Aof 1th8e8 .r5ig ihnt. 2cone. B
18. 3 12 km 19. 8m 21. SVV555 4 61211287..4865.71 c cmmm323, 2.CA WhEFic11h eVVqu55atFEio11n r 22ep reDBsentsFF E11uleVEr’55s TEVhe21or e22m?A BCD 244009480...240 19i nii.nn2..22 12 in.
7m 22. 238.60 m3 3. The two-dimensional representation of the 9. Find the volume of a 6-inch tall glass with a
Fairned r etghue lsaur rafnadce t haere par aisnmds v, oclounmees ,o afn tdh ec ysloinlidde. rTsh aer ep yrirgahmti.d s 23. 327.6 ft3 Afa cleaste oraf la a preoaly hedronB is c aslulrefda c e ? a r e. aD A3- i4n2c.h4 1d iianm.3eter. A B 169.56 in.3
Round your answer to two decimal places, if necessary. 24. 600(cid:58) yd2 C lateral edge D a net C 54 in.3 D 56.52 in.3
20. 12m 21. 5 cm 25. 1024(cid:58) m3 4. Find the surface 10. Find the volume of the solid
8 cm area of the right prism. (in cubic meters). D
11m B 8 ft 30 ft
22 ft
8 cm A 855.07 ft2 B 1733.07 ft2
5m C 1342.47 ft2 D 2625.68 ft2 6.5
Friignhdt .t hReo uvonldu myoeu or fa nthsew seor ltido. tTwhoe dceycliinmdaelr ps laancdes p, riifs nmesc easres ary. 5. Find the surface area 20 cm 33 33 10
of the right cylinder. 6
22. 8m 23. 1.6 ft 2 ft A 17 cm A 780 m3 B 840 m3
0.9m
7 ft A 4649.6 cm2 B 2960 cm2 C 570 m3 D 960 m3
5m
C 2323.6 cm2 D 1480 cm2 11. Find the volume of
the pyramid. B
5 ft
24. Two cones have a scale factor of 2:5. The sma1l0l efrt cone has a surface 6. Apwo ipltyhog layo hcneo admnromdn to hinne vwlaehtretiercaxhl itfsha eac eb sa ?as er e .i str Caia ngles BA 516760.06 7ft 3ft3 17 ft
25. aWTrweroait eos pfy h9oe6ur(cid:58)re sa s nhqsauwvaeer rea i ynsac traedlresm. fFsa icontfod r(cid:58) t ho.ef 3su:r8f.a Tceh ea rsema aolfl etrh esp lhaergree rh caos nae . AC ppyrirsamm id DB dcoondeecahedron CD 288530. 3ft33 ft3 10 ft
volume of about 54(cid:58) cubic meters. Find the volume of the larger
sphere. Write your answer in terms of (cid:58).
Geometry Geometry
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CH1AP2TER Standardized Test B continued CH1AP2TER Performance Assessment
For use For use after Chapter 12 For use after Chapter 12
12. Find the volume 17. Which prism is similar to a prism with a Journal 1. Without using variables, explain how to fi nd the volumes of right prisms,
of the cone.B length of 5 inches, width of 2 inches, and a right cylinders, regular pyramids, right cones, and spheres.
A 234.45 in.3 10 in. 14 in. height of 2 }12 inches? D
B 167.55 in.3 Al5 4 in., w5 1 in., h5 1 } 12 in. MuPlrtoi-bSlteemp 2. Aco mrepadacyt- tcoa-radsbseomarbdl eb ohxoems.e furnishings company packages its products in
C 502.4 in.3 4 in.
D 334.94 in.3 Bl5 10 in., w5 7 in., h5 7 } 12 in. a. Apr idsimni. nTgh tea bbloex i sis p 5a cfkeeatg leodn ign, a3 bfeoext twhaidt eis, ainn dth 1e fsohoatp dee oefp .a Friencdta tnhgeu vlaorl ume
13.A Tfrh osemp sh eaet rgoeif v aelnl ppooiinntt si si Bna s p a?pc le a. neAqeuidistant CDll55 120 i nin.,. ,w w55 } 45 4 i nin.,. ,h h55 1 4 i n} 12. in. b. aAshn odtrw aspnue.r fzFaoicniedd aa tlrh edeae vsokof l itushm ep eab cookxfa .tgheed b ionx t.he box 43fftt 1.5ft
C circle D great circle Gridded Response
5 8 8
14. Find the surface area of a globe with a 18. Find the volume 2ft
24-inch diameter. A of the solid. c. A cylindrical side table is packaged in the 12 in.
A 1809.56 in.2 B 7234.56 in.2 4 ft rectangular prism as shown. How much
space is not taken up by the table inside
C 904.32 in.2 D 3627.28 in.2 the box? 18 in.
16 in.
15. If an intersecting plane contains the center of 15 ft
a sphere, then the intersection is a 14 in.
? of the sphere. D 14 in.
A hemisphere B great sphere d. The company also sells hanging lights like
C half circle D great circle 6 ft the one shown. The right cones are similar
Short Response with a scale factor of 3:5. The surface
16. Find the volume of the solid. C area of the smaller cone is approximately
19. A ball has a 10-inch radius. 61.2 square inches and the volume of the
3 cm a. Find the volume of the ball.4188.79 in.2 smaller cone is approximately 31.8 cubic
inches. Find the volume and surface area
b. Find the volume of a ball with half the of the larger cone.
8 cm rlaardgieurs .b Iasl lt?h eE xvpollauimn.e hNaolf; 5th2a3t. 6o0f tihne.3 e. The leg of a couch that the company
sells is formed by cutting off the top
Extended Response one-third of a pyramid as shown.
A 226.08 cm3 B 188.4 cm3 20. A stainless steel tank is 8 feet tall with a Explain how to fi nd the volume of
C 113.10 cm3 D 141.3 cm3 12-foot diameter. 527.79 ft2 the couch leg.
a. Find the surface area of the tank.
b. Find the volume of the tank.904.78 ft3
c. How long will it take to drain }78 of a tank 1Fi.nFdi nthde t hveo lvuomluem oef ao fr eag ruiglahrt ppyrriasmm iodr o rri grhigt hcty clionndee rb yb yfi nmduinltgip olynien gth tihrde oarfe tah eo fp trhoed ubcats eo fb tyh eth aer ehae iogfh t.
at a rate of 3.5 cubic feet per minute? the base and the height. Find the area of a sphere by fi nding four thirds of the product of pi and the
d. If carbonated water and corn syru2p2 6.2 min cube of the radius.
are mixed at a 5:2 ratio, how much of 2. a. 15 ft3; 46 ft2b. 13.5 ft3c. about 1718.44 in.3d.about 147.22 in.3; 170 in.2
each do you need to fi ll the tank? e.Subtract the volume of the pyramid that is cut off from the main pyramid.
water: 646.27 ft3; syrup; 258.51 ft3
Geometry Geometry
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