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Volume?MODULEESSENTIAL QUESTIONHow can you use volumeto solve real-worldproblems?13LESSON 13.1Volume of Cylinders8.G.9LESSON 13.2Volume of Cones8.G.9LESSON 13.3Volume of Spheres Houghton Mifflin Harcourt Publishing Company Image Credits: LOOK Die Bildagentur der FotografenGmbH/Alamy8.G.9Real-World VideoAquariums are in the shape of cylinders andrectangular prisms. To find out how much water anaquarium holds, you can use formulas for volume.my.hrw.commy.hrw.commy.hrw.comMath On the SpotAnimated MathPersonal Math TrainerGo digital with yourwrite-in studentedition, accessible onany device.Scan with your smartphone to jump directlyto the online edition,video tutor, and more.Interactively explorekey concepts to seehow math works.Get immediatefeedback and help asyou work throughpractice sets.397
Are YOU Ready?PersonalMath TrainerComplete these exercises to review skills you will needfor this module.ExponentsEXAMPLEmy.hrw.comOnline Practiceand HelpMultiply the base (6) by itself the number oftimes indicated by the exponent (3).63 6 6 6 36 6 216Find the product of the first two terms.Find the product of all the terms.Evaluate each exponential expression.1. 1122. 253.5. 2.136. 0.137.( 15 )9.6(3 )324. (0.3)28. 1003Round DecimalsEXAMPLERound 43.2685 to the underlinedplace.43.268543.27The digit to be rounded: 6The digit to its right is 8.8 is 5 or greater, so round up.The rounded number is 43.27.9. 2.37410. 126.39911. 13.957712. 42.69013. 134.9514. 2.048615. 63.635216. 98.9499Simplify Numerical ExpressionsEXAMPLE1(3.14) (4)2 (3) 13 (3.14) (16) (3)3 50.24Simplify the exponent.Multiply from left to right.Simplify each expression.398Unit 517. 3.14 (5)2 (10)18. 13 (3.14) (3)2 (5)19. 43 (3.14) (3)320. 43 (3.14) (6)321. 3.14 (4)2 (9)22. 13 (3.14) (9)2 23() Houghton Mifflin Harcourt Publishing CompanyRound to the underlined place.
Reading Start-UpVisualize VocabularyUse the words to complete the empty columns in the chart.You may use words more than once.ShapeDistance Around Attributescircler, dsquare90 corner,sidesrectangle90 corner,sidesAssociated ReviewWordsUnderstand VocabularyVocabularyReview Wordsarea (área)base (base,en numeración) circumference(circunferencia) diameter (diámetro)height (altura) length (longitud) perimeter (perímetro) radius (radio) right angle (ángulo recto) width (ancho)Preview Wordscone (cono)cylinder (cilindro)sphere (esfera)Complete the sentences using the preview words.1. A three-dimensional figure that has one vertex and one circularbase is a.2. A three-dimensional figure with all points the same distancefrom the center is a. Houghton Mifflin Harcourt Publishing Company3. A three-dimensional figure that has two congruent circular basesis a.Active ReadingThree-Panel Flip Chart Before beginning themodule, create a three-panel flip chart to helpyou organize what you learn. Label each flapwith one of the lesson titles from this module.As you study each lesson, write importantideas like vocabulary, properties, and formulasunder the appropriate flap.Module 13399
GETTING READY FORVolumeUnderstanding the standards and the vocabulary terms in the standardswill help you know exactly what you are expected to learn in this module.Know the formulas for thevolumes of cones, cylinders, andspheres and use them to solvereal-world and mathematicalproblems.Key Vocabularyvolume (volumen)The number of cubic unitsneeded to fill a given space.cylinder (cilindro)A three-dimensional figurewith two parallel, congruentcircular bases connected by acurved lateral surface.8.G.9Know the formulas for thevolumes of cones, cylinders, andspheres and use them to solvereal-world and mathematicalproblems.What It Means to YouYou will learn the formula for the volume of a cylinder.EXAMPLE 8.G.9The Asano Taiko Company of Japan built the world’s largestdrum in 2000. The drum’s diameter is 4.8 meters, and its height is4.95 meters. Estimate the volume of the drum.d 4.8 5h 4.95 5What It Means to YouYou will learn formulas for the volume of a cone and a sphere.EXAMPLE 8.G.9Find the volume of the cone. Use 3.14 for π.2 in.400Unit 5 18.75 · 5The volume of the drum is approximately 94 m3.cone (cono)A three-dimensional figure withone vertex and one circular base.my.hrw.com (3) (6.25) (5)Use 3 for π. 93.75 946 in.Visit my.hrw.comto see all CACommon CoreStandardsunpacked.Volume of a cylinder (3) (2.5)2 · 5r d2 52 2.5Key Vocabularysphere (esfera)A three-dimensional figurewith all points the samedistance from the center.V (πr2)hB π(22) 4π in2V 13 · 4π · 6V 8π 25.1 in31 BhV 3Use 3.14 for π.The volume of the cone is approximately 25.1 in3.The volume of a sphere with the same radius isV 43 πr 3 43 (3)(2)3 32 in3. Houghton Mifflin Harcourt Publishing Company8.G.9
LESSON13.1 Volume of Cylinders?8.G.9Know the formulas for thevolumes of cones, cylinders,and spheres and use themto solve real-world andmathematical problems.ESSENTIAL QUESTIONHow do you find the volume of a cylinder?EXPLORE ACTIVITY8.G.9Modeling the Volume of a CylinderA cylinder is a three-dimensional figure that has two congruent circular basesthat lie in parallel planes. The volume of any three-dimensional figure is thenumber of cubic units needed to fill the space taken up by the solid figure.One cube represents one cubic unit of volume. You can develop theformula for the volume of a cylinder using an empty soup can or othercylindrical container. First, remove one of the bases.A Arrange centimeter cubes in a single layer at the bottom of thecylinder. Fit as many cubes into the layer as possible. How many cubesare in this layer? Houghton Mifflin Harcourt Publishing CompanyB To find how many layers of cubes fit in the cylinder, make a stackof cubes along the inside of the cylinder. How many layers fit in thecylinder?C How can you use what you know to find the approximate numberof cubes that would fit in the cylinder?Reflect1. Make a Conjecture Suppose you know the area of the base of a cylinderand the height of the cylinder. How can you find the cylinder’s volume?2. Let the area of the base of a cylinder be B and the height ofthe cylinder be h. Write a formula for the cylinder’s volume V.Lesson 13.1401
Finding the Volume of a CylinderUsing a FormulaMath On the Spotmy.hrw.comFinding volumes of cylinders is similar to finding volumes of prisms. You findthe volume V of both a prism and a cylinder by multiplying the height h by thearea of the base B, so V Bh.The base of a cylinder is a circle, so for a cylinder, B πr2.Volume of a CylinderThe volume V of a cylinder withradius r is the area of the baseB times the height h.hrV Bh or V πr2hEXAMPLE 18.G.9Find the volume of each cylinder. Round your answers to the nearesttenth if necessary. Use 3.14 for π.AV πr2h10 in.AnimatedMath3 in.my.hrw.com 3.14 · 32 · 10Substitute. 3.14 · 9 · 10Simplify. 282.6Multiply.The volume is about 282.6 in3.13 cmSince the diameteris 6.4 cm, the radiusis 3.2 cm.Recall that thediameter of a circle istwice the radius, sod2r d and r .2V πr2h 3.14 · 3.22 · 13Substitute. 3.14 · 10.24 · 13Simplify. 418Multiply.The volume is about 418 cm3.Reflect3. What If? If you want a formula for the volume of a cylinder that involvesthe diameter d instead of the radius r, how can you rewrite it?402Unit 5 Houghton Mifflin Harcourt Publishing CompanyB 6.4 cm
YOUR TURNFind the volume of each cylinder. Round your answers to the nearesttenth if necessary. Use 3.14 for π.4.PersonalMath TrainerOnline Practiceand Help5.6 in.my.hrw.com4 ft10 in.12 ftFinding the Volume of a Cylinderin a Real-World ContextYou can find the volume of a bass drum by using the formula for the volumeof a cylinder.Math On the Spotmy.hrw.comEXAMPL 2EXAMPLE8.G.9 Houghton Mifflin Harcourt Publishing Company Image Credits: Stephen Dunn/Getty Images Sports/Getty ImagesOne of the bass drums used in a marching band has a diameter of18 inches and a depth of 14 inches. Find the volume of the drumto the nearest tenth. Use 3.14 for π.STEP 1Find the radius of the drum.d 18 9 in.r 22STEP 2Find the volume of the drum.V πr2h 3.14 · 92 · 14Substitute. 3.14 · 81 · 14Simplify the exponent. 3560.76Multiply.The volume of the drum is about 3560.8 in3.YOUR TURN6. A drum company advertises a snare drum that is 4 inches high and12 inches in diameter. Find the volume of the drum to the nearesttenth. Use 3.14 for π.PersonalMath TrainerOnline Practiceand Helpmy.hrw.comLesson 13.1403
Guided Practice1. Vocabulary Describe the bases of a cylinder. (Explore Activity)2. Figure 1 shows a view from above of inch cubes on the bottomof a cylinder. Figure 2 shows the highest stack of cubes that willfit inside the cylinder. Estimate the volume of the cylinder. Explainyour reasoning. (Explore Activity)Figure 1Figure 23. Find the volume of the cylinder to the nearest tenth. Use 3.14 for π.(Example 1)V πr2hV π · 3.14 ·6m2·15 m· The volume of the cylinder is approximatelym3.The radius of the drum is aboutThe volume of the drum is about?m.m3.ESSENTIAL QUESTION CHECK-IN5. How do you find the volume of a cylinder? Describe which measurementsof a cylinder you need to know.404Unit 5 Houghton Mifflin Harcourt Publishing Company4. A Japanese odaiko is a very large drum that is made by hollowing out asection of a tree trunk. A museum in Takayama City has three odaikos ofsimilar size carved from a single tree trunk. The largest measures about2.7 meters in both diameter and length, and weighs about 4.5 metric tons.Using the volume formula for a cylinder, approximate the volume of thedrum to the nearest tenth. (Example 2)
NameClassDate13.1 Independent PracticePersonalMath Trainer8.G.9my.hrw.comOnline Practiceand HelpFind the volume of each figure. Round your answers to the nearesttenth if necessary. Use 3.14 for π.6.7.1.5 cm4 in.24 in.11 cm8.5m16 m9.10 in.12 in. Houghton Mifflin Harcourt Publishing Company Image Credits: Tim Laman/National Geographic/GettyImages10. A cylinder has a radius of 4 centimetersand a height of 40 centimeters.11. A cylinder has a radius of 8 meters anda height of 4 meters.Round your answer to the nearest tenth, if necessary. Use 3.14 for π.12. The cylindrical Giant Ocean Tank at the New EnglandAquarium in Boston is 24 feet deep and has a radiusof 18.8 feet. Find the volume of the tank.13. A standard-size bass drum has a diameter of 22 inchesand is 18 inches deep. Find the volume of this drum.14. Grain is stored in cylindrical structures called silos. Findthe volume of a silo with a diameter of 11.1 feet and aheight of 20 feet.15. The Frank Erwin Center, or “The Drum,” at the University of Texas in Austincan be approximated by a cylinder that is 120 meters in diameter and30 meters in height. Find its volume.Lesson 13.1405
16. A barrel of crude oil contains about 5.61 cubic feet of oil. How manybarrels of oil are contained in 1 mile (5280 feet) of a pipeline that has aninside diameter of 6 inches and is completely filled with oil? How much is“1 mile” of oil in this pipeline worth at a price of 100 per barrel?17. A pan for baking French bread is shaped like half a cylinder. It is12 inches long and 3.5 inches in diameter. What is the volume ofuncooked dough that would fill this pan?3.5 in.12 in.FOCUS ON HIGHER ORDER THINKING18. Explain the Error A student said the volume of a cylinder with a3-inch diameter is two times the volume of a cylinder with the sameheight and a 1.5-inch radius. What is the error?Work Area20. Analyze Relationships Cylinder A has a radius of 6 centimeters.Cylinder B has the same height and a radius half as long as cylinder A.What fraction of the volume of cylinder A is the volume of cylinder B?Explain.406Unit 5 Houghton Mifflin Harcourt Publishing Company19. Communicate Mathematical Ideas Explain how you can find theheight of a cylinder if you know the diameter and the volume. Includean example with your explanation.
LESSON13.2 Volume of Cones?8.G.9Know the formulas for thevolumes of cones, cylinders,and spheres and use themto solve real-world andmathematical problems.ESSENTIAL QUESTIONHow do you find the volume of a cone?EXPLORE ACTIVITY8.G.9Modeling the Volume of a ConeA cone is a three-dimensional figure that has one vertex and one circular base.To explore the volume of a cone, Sandi does an experiment with acone and a cylinder that have congruent bases and heights. She fillsthe cone with popcorn kernels and then pours the kernels into thecylinder. She repeats this until the cylinder is full.Sandi finds that it takes 3 cones to fill the volume of the cylinder.STEP 1What is the formula for the volume V of acylinder with base area B and height h?STEP 2What is the area of the base of the cone?STEP 3Sandi found that, when the bases and height are the same,times Vcone Vcylinder. Houghton Mifflin Harcourt Publishing CompanySTEP 4How does the volume of the cone compare to the volume of thecylinder?Volume of the cone:Vcone · VcylinderReflect1.Use the conclusion from this experiment to write a formula for thevolume of a cone in terms of the height and the radius. Explain.Lesson 13.2407
Finding the Volume of a ConeUsing a FormulaMath On the Spotmy.hrw.comThe formulas for the volume of a prism and the volume of a cylinder are thesame: multiply the height h by the area of the base B, so V Bh.In the Explore Activity, you saw that the volume of a cone is one third thevolume of a cylinder with the same base and height.Volume of a ConeThe volume V of a cone withradius r is one third the area ofthe base B times the height h.h1 Bh or V 1 πr2hV 33rEXAMPLE 18.G.9Find the volume of each cone. Round your answers to the nearest tenth.Use 3.14 for π.V 13 πr2hMath TalkMathematical Practices8 in.How can you estimatethe volume of anycone?2 in. 13 · 3.14 · 22 · 8Substitute. 13 · 3.14 · 4 · 8Simplify. 33.5Multiply.The volume is about 33.5 in3.B Since the diameter is 8 ft, the radius is 4 ft.V 13 πr2h9 ft8 ft 13 · 3.14 · 42 · 9Substitute. 13 · 3.14 · 16 · 9Simplify. 150.7Multiply.The volume is about 150.7 ft3.Reflect2.408Unit 5How can you rewrite the formula for the volume ofa cone using the diameter d instead of the radius r? Houghton Mifflin Harcourt Publishing CompanyA
YOUR TURNFind the volume of each cone. Round your answers to the nearest tenth.Use 3.14 for π.15 cm3.4.PersonalMath TrainerOnline Practiceand Help3 ftmy.hrw.com2 ft16 cmFinding the Volume of a VolcanoThe mountain created by a volcano is often cone–shaped.EXAMPL 2EXAMPLE8.G.9 Houghton Mifflin Harcourt Publishing Company Image Credits: Marco Regalia Sell/Alamy ImagesFor her geography project, Karen built a clay model of avolcano in the shape of a cone. Her model has a diameterof 12 inches and a height of 8 inches. Find the volume ofclay in her model to the nearest tenth. Use 3.14 for π.STEP 1Math On the Spotmy.hrw.comFind the radius.12 6 in.r 2STEP 2Find the volume of clay.V 13 πr2h 13 · 3.14 · 62 · 8Substitute. 13 · 3.14 · 36 · 8Simplify. 301.44Multiply.The volume of the clay is about 301.4 in3.YOUR TURN5. The cone of the volcano Parícutin in Mexico had a height of 410 metersand a diameter of 424 meters. Find the volume of the cone to thenearest tenth. Use 3.14 for π.PersonalMath TrainerOnline Practiceand Helpmy.hrw.comLesson 13.2409
Guided Practice1. The area of the base of a cylinder is 45square inches and its height is 10 inches.A cone has the same area for its base andthe same height. What is the volume of thecone? (Explore Activity)Vcylinder Bh ·2. A cone and a cylinder have congruent heightand bases. The volume of the cone is 18 m3.What is the volume of the cylinder? Explain.(Explore Activity) 1VVcone 3 cylinder1 3 The volume of the cone isin3.Find the volume of each cone. Round your answer to the nearest tenth ifnecessary. Use 3.14 for π. (Example 1)3.4.7 ft100 in.33 in.6 ft6. A cone-shaped building is commonly used to store sand. What would bethe volume of a cone-shaped building with a diameter of 50 meters and aheight of 20 meters? Round your answer to the nearest tenth. Use 3.14 for π.(Example 2)?ESSENTIAL QUESTION CHECK-IN7. How do you find the volume of a cone?410Unit 5 Houghton Mifflin Harcourt Publishing Company5. Gretchen made a paper cone to hold a gift for a friend. The paper conewas 15 inches high and had a radius of 3 inches. Find the volume of thepaper cone to the nearest tenth. Use 3.14 for π. (Example 2)
NameClassDate13.2 Independent PracticePersonalMath Trainer8.G.9my.hrw.comFind the volume of each cone. Round youranswers to the nearest tenth if necessary.Use 3.14 for π.8.7 mm8 mm9.6 in.Online Practiceand Help13. A snack bar sells popcorn in cone-shapedcontainers. One container has a diameterof 8 inches and a height of 10 inches. Howmany cubic inches of popcorn does thecontainer hold?14. A volcanic cone has a diameter of300 meters and a height of 150 meters.What is the volume of the cone?15. Multistep Orange traffic cones come in avariety of sizes. Approximate the volume,in cubic inches, of a traffic cone that hasa height of 2 feet and a diameter of10 inches. Use 3.14 for π.2 in.Find the missing measure for each cone.Round your answers to the nearest tenthif necessary. Use 3.14 for π.10. A cone has a diameter of 6 centimetersand a height of 11.5 centimeters.16. radius height 6 in. Houghton Mifflin Harcourt Publishing Companyvolume 100.48 in311. A cone has a radius of 3 meters and aheight of 10 meters.17. diameter 6 cmheight volume 56.52 cm3Round your answers to the nearest tenthif necessary. Use 3.14 for π.12. Antonio is making mini waffle cones. Eachwaffle cone is 3 inches high and has aradius of 34 inch. What is the volume of awaffle cone?18. The diameter of a cone-shaped containeris 4 inches, and its height is 6 inches. Howmuch greater is the volume of a cylindershaped container with the same diameterand height? Round your answer to thenearest hundredth. Use 3.14 for π.Lesson 13.2411
FOCUS ON HIGHER ORDER THINKINGWork Area19. Alex wants to know the volume of sand in anhourglass. When all the sand is in the bottom,he stands a ruler up beside the hourglass andestimates the height of the cone of sand.a. What else does he need to measure to findthe volume of sand?b. Make a Conjecture If the volume ofsand is increasing at a constant rate, is theheight increasing at a constant rate? Explain.20. Problem Solving The diameter of a cone is x cm, the height is 18 cm,and the volume is 301.44 cm3. What is x? Use 3.14 for π.22. Critique Reasoning Herb knows that the volume of a cone is one thirdthat of a cylinder with the same base and height. He reasons that a conewith the same height as a given cylinder but 3 times the radius shouldtherefore have the same volume as the cylinder, since 13 3 1. Is Herbcorrect? Explain.412Unit 5 Houghton Mifflin Harcourt Publishing Company21. Analyze Relationships A cone has a radius of 1 foot and a height of2 feet. How many cones of liquid would it take to fill a cylinder with adiameter of 2 feet and a height of 2 feet? Explain.
LESSON13.3 Volume of Spheres?8.G.9Know the formulas for thevolumes of cones, cylinders,and spheres and use themto solve real-world andmathematical problems.ESSENTIAL QUESTIONHow do you find the volume of a sphere?EXPLORE ACTIVITY8.G.9Modeling the Volume of a SphereA sphere is a three-dimensional figure with all points the same distancefrom the center. The radius of a sphere is the distance from the center to anypoint on the sphere.You have seen that a cone fills 13 of a cylinder of the same radius and height h.If you were to do a similar experiment with a sphere of the same radius, youwould find that a sphere fills 23 of the cylinder. The cylinder’s height is equal totwice the radius of the sphere.h 2rr Houghton Mifflin Harcourt Publishing CompanySTEP 1h 2rrh 2rrWrite the formula V Bh for each shape. Use B πr2 andsubstitute the fractions you know for the cone and sphere.CylinderConeSphereV πr 2h1 πr 2hV 32 πr 2hV 3STEP 2Notice that a sphere always has a heightequal to twice the radius. Substitute 2r for h.2 πr 2(2r)V 3STEP 3Simplify this formula for the volume of a sphere.V πr 3Reflect1.Analyze Relationships A cone has a radius of r and a height of 2r. Asphere has a radius of r. Compare the volume of the sphere and cone.Lesson 13.3413
Finding the Volume of a SphereUsing a FormulaThe Explore Activity illustrates a formula for the volume of a sphere with radius r.Math On the Spotmy.hrw.comVolume of a SphereThe volume V of a sphere is 43 πtimes the cube of the radius r.rV 43 πr3EXAMPLE 18.G.9Find the volume of each sphere. Round your answers to the nearest tenthif necessary. Use 3.14 for π.A2.1 cmMath TalkMathematical Practices 43 · 3.14 · 2.13Substitute. 43 · 3.14 · 9.26Simplify. 38.8Multiply.The volume is about 38.8 cm3.B7 cmSince the diameter is 7 cm,the radius is 3.5 cm.V 43 πr 3 43 · 3.14 · 3.53Substitute. 43 · 3.14 · 42.9Simplify. 179.6Multiply.The volume is about 179.6 cm3.YOUR TURNPersonalMath TrainerOnline Practiceand Helpmy.hrw.com414Unit 5Find the volume of each sphere. Round your answers to the nearest tenth.Use 3.14 for π.2. A sphere has a radius of 10 centimeters.3. A sphere has a diameter of 3.4 meters. Houghton Mifflin Harcourt Publishing CompanyIf you know the diameterof a sphere, how would theformula for the volume ofa sphere be written interms of d?V 43 πr 3
Finding the Volume of a Spherein a Real-World ContextMany sports, including golf and tennis, use a ball that is spherical in shape.Math On the SpotEXAMPL 2EXAMPLE8.G.9my.hrw.comSoccer balls come in several different sizes. One soccer ball has a diameterof 22 centimeters. What is the volume of this soccer ball? Round youranswer to the nearest tenth. Use 3.14 for π.STEP 1Find the radius.r d2 11 cmSTEP 2Find the volume of the soccer ball.V 43 πr 3 43 · 3.14 · 113Substitute. 43 · 3.14 · 1331Simplify. 5572.4533Multiply.The volume of the soccer ball is about 5572.5 cm3.Reflect Houghton Mifflin Harcourt Publishing Company Image Credits: PhotoDisc/Getty Images4.What is the volume of the soccer ball in terms of π, to the nearestwhole number multiple? Explain your answer.5. Analyze Relationships The diameter of a basketball is about 1.1 timesthat of a soccer ball. The diameter of a tennis ball is about 0.3 times thatof a soccer ball. How do the volumes of these balls compare to that of asoccer ball? Explain.YOUR TURN6. Val measures the diameter of a ball as 12 inches. How many cubicinches of air does this ball hold, to the nearest tenth? Use 3.14 for π.PersonalMath TrainerOnline Practiceand Helpmy.hrw.comLesson 13.3415
Guided Practice1. Vocabulary A sphere is a three-dimensional figure with all pointsfrom the center. (Explore Activity)2. Vocabulary Theis the distance from the centerof a sphere to a point on the sphere. (Explore Activity)Find the volume of each sphere. Round your answers to the nearest tenthif necessary. Use 3.14 for π. (Example 1)3.1 in.4.20 cm5. A sphere has a radius of 1.5 feet.6. A sphere has a diameter of 2 yards.7. A baseball has a diameter of 2.9 inches. Find the volume of thebaseball. Round your answer to the nearest tenth if necessary.Use 3.14 for π. (Example 2)8. A basketball has a radius of 4.7 inches. What is its volume to thenearest cubic inch. Use 3.14 for π. (Example 2)9. A company is deciding whether to package a ballin a cubic box or a cylindrical box. In either case,the ball will touch the bottom, top, and sides.(Explore Activity)rrb. Find an expression for the volume of the cubic box.c. About what portion of the space inside the cubic box is empty? Explain.?ESSENTIAL QUESTION CHECK-IN10. Explain the steps you use to find the volume of a sphere.416Unit 5 Houghton Mifflin Harcourt Publishing Companya. What portion of the space inside the cylindricalbox is empty? Explain.
NameClassDate13.3 Independent Practice8.G.9PersonalMath Trainermy.hrw.comFind the volume of each sphere. Round youranswers to the nearest tenth if necessary.Use 3.14 for π.11. radius of 3.1 meters12. diameter of 18 inchesOnline Practiceand Help19. Fossilized spherical eggs of dinosaurscalled titanosaurid sauropods werefound in Patagonia. These eggs were15 centimeters in diameter. Find thevolume of an egg. Round your answer tothe nearest tenth.13. r 6 in.14. d 36 m15.16.11 cm2.5 ft20. Persevere in Problem Solving An ostrichegg has about the same volume as asphere with a diameter of 5 inches. If the1eggshell is aboutinch thick, find the12volume of just the shell, not including theinterior of the egg. Round your answer tothe nearest tenth.21. Multistep Write the stepsyou would use to find aformula for the volume ofthe figure at right. Thenwrite the formula.rrr Houghton Mifflin Harcourt Publishing CompanyThe eggs of birds and other animals come inmany different shapes and sizes. Eggs oftenhave a shape that is nearly spherical. Whenthis is true, you can use the formula for asphere to find their volume.17. The green turtle lays eggs that areapproximately spherical with an averagediameter of 4.5 centimeters. Each turtlelays an average of 113 eggs at one time.Find the total volume of these eggs, to thenearest cubic centimeter.18. Hummingbirds lay eggs that are nearlyspherical and about 1 centimeter indiameter. Find the volume of an egg.Round your answer to the nearest tenth.Lesson 13.3417
22. Critical Thinking Explain what happens to the volume of a sphere if youdouble the radius.23. Multistep A cylindrical can of tennis balls holds a stack of three balls sothat they touch the can at the top, bottom, and sides. The radius of eachball is 1.25 inches. Find the volume inside the can that is not taken up bythe three tennis balls.FOCUS ON HIGHER ORDER THINKINGWork Area24. Critique Reasoning A sphere has a radius of 4 inches, and a cube-shapedbox has an edge length of 7.5 inches. J.D. says the box has a greatervolume, so the sphere will fit in the box. Is he correct? Explain.26. Analyze Relationships Hari has models of a sphere, a cylinder, and acone. The sphere’s diameter and the cylinder’s height are the same, 2r. Thecylinder has radius r. The cone has diameter 2r and height 2r. Compare thevolumes of the cone and the sphere to the volume of the cylinder.27. A spherical helium balloon that is 8 feet in diameter can lift about 17pounds. What does the diameter of a balloon need to be to lift a personwho weighs 136 pounds? Explain.418Unit 5 Houghton Mifflin Harcourt Publishing Company25. Critical Thinking Which would hold the most water: a bowl in the shapeof a hemisphere with radius r, a cylindrical glass with radius r and height r,or a cone-shaped drinking cup with radius r and height r? Explain.
MODULE QUIZReadyPersonalMath Trainer13.1 Volume of CylindersOnline Practiceand HelpFind the volume of each cylinder. Round your answers to thenearest tenth if necessary. Use 3.14 for π.1. 6 ftmy.hrw.com2. A can of juice has a radius of 4 inchesand a height of 7 inches. What is thevolume of the can?8 ft13.2 Volume of ConesFind the volume of each cone. Round your answers to thenearest tenth if necessary. Use 3.14 for π.3.4.15 cm20 in.6 cm12 in.13.3 Volume of SpheresFind the volume of each sphere. Round your answers to thenearest tenth if necessary. Use 3.14 for π. Houghton Mifflin Harcourt Publishing Company5.3 ft6.13 cmESSENTIAL QUESTION7. What measurements do you need to know to find the volume of acylinder? a cone? a sphere?Module 13419
MODULE 13MIXED REVIEWPersonalMath TrainerAssessment Readiness2NoB. (1.5, –6)YesNoC. (3, 0)YesNoKx-2Select Yes or No for A–C.YesOnline Practiceand Helpy1. Triangle JKL is dilated by a scale factor of 1.5 withthe origin as the center of dilation. Look at eachordered pair. Does the ordered pair represent avertex of the image?A. (–3, –4.5)my.hrw.comO2-2J -4L2. A sphere has a radius of 4 inches.Choose True or False for each statement.A. A sphere with half the radius has 81of the volume.B. A sphere with twice the radius has6 times the volume.C. A sphere with 3 times the radius has27 times the volume.TrueFalseTrueFalseTrueFalse4. A cylindrical drinking glass has a base radius of 3.2 centimetersand a height of 14.0 centimeters. Given that 1 cubic centimeteris equivalent to 1 milliliter, how many milliliters of water doesthe glass hold when it is 34 full? Round to the nearest milliliter.14.0 cm3.2 cm420Unit 5 Houghton Mifflin Harcourt Publishing Company3. A pile of sand is shaped like a cone with a height of 4 feet and a basediameter of 13 feet. Each cubic foot of sand weighs 90 pounds. Does the pileof sand weigh more than a ton (2000 pounds)? Explain how you know.
Math On the Spot my.hrw.com Math Trainer Online Practice and Help Personal my.hrw.com Math Trainer Online Practice and Help Personal my.hrw.com Find the volume of each cylinder. Round your answers to the nearest tenth if necessary. Use 3.14 for π. 4. 5. Finding the Volume of a Cylinder in a Real-World Context
