Lesson 14.1 Skills Practice

Transcription

1 Lesson 14.1 Skills Practice Name Date Drum Roll, Please! Volume of a Cylinder Vocabulary Explain why the term describes each given figure. 1. cylinder 2. right circular cylinder Chapter 14 Skills Practice 921

2 Lesson 14.1 Skills Practice page 2 3. radius and height of the cylinder r h Problem Set Identify the radius, diameter, and height of each cylinder cm 2. 7 m 10 cm 15 m Radius: 4 cm Diameter: 8 cm Height: 10 cm 922 Chapter 14 Skills Practice

3 Lesson 14.1 Skills Practice page 3 Name Date ft in. 12 ft 9 in mm 6. 4 yd 12 yd 8 mm Chapter 14 Skills Practice 923

4 Lesson 14.1 Skills Practice page 4 Calculate and use the area of the base to determine the volume of each given cylinder. Use 3.14 for π cm 5 cm The area of each base is π? 2 2 < 3.14? 4 < cm 2. The volume is 12.56? 5 < cm cm 3 cm 924 Chapter 14 Skills Practice

5 Lesson 14.1 Skills Practice page 5 Name Date 9. 8 ft 7 ft yd 4 yd Chapter 14 Skills Practice 925

6 Lesson 14.1 Skills Practice page cm 10 cm ft 5 ft 926 Chapter 14 Skills Practice

7 Lesson 14.1 Skills Practice page 7 Name Date Calculate the volume of each cylinder. Use 3.14 for π. Round decimals to the nearest tenth, if necessary m yd 7 m 22 yd V 5 πr 2 h V 5 π(5.5) 2 (7) V π V < m m ft 5 m 4.5 ft Chapter 14 Skills Practice 927

8 Lesson 14.1 Skills Practice page mm ft 6 mm 5 ft m cm 12 m 13 cm 928 Chapter 14 Skills Practice

9 Lesson 14.2 Skills Practice Name Date Piling On! Volume of a Cone Vocabulary Draw a diagram to illustrate each key term. 1. cone (identify the vertex and the base) 2. height of a cone Chapter 14 Skills Practice 929

10 Lesson 14.2 Skills Practice page 2 Problem Set Identify the radius, diameter, and height of each cone. 1. h = 6 mm r = 5 mm m 12 m Radius: 5 mm Diameter: 10 mm Height: 6 mm ft 4. 7 ft 11 yd 4 yd 930 Chapter 14 Skills Practice

11 Lesson 14.2 Skills Practice page 3 Name Date 5. 6 m 6. [ 3 ft ] 3 ft [ 8 m ] 7. 8 in mm 5 mm 3 in. Chapter 14 Skills Practice 931

12 Lesson 14.2 Skills Practice page 4 Calculate the volume of each cone. Use 3.14 for π cm 4 cm The area of the base is π? π? 16 < cm 2. 1 The volume of the cone is (50.24? 5) (251.20) < cm cm 7 cm in. 3 in. 932 Chapter 14 Skills Practice

13 Lesson 14.2 Skills Practice page 5 Name Date in. 4 in m 15 m mm 14 mm Chapter 14 Skills Practice 933

14 Lesson 14.2 Skills Practice page cm 6.5 cm cm 1 cm ft 4.5 ft 934 Chapter 14 Skills Practice

15 Lesson 14.2 Skills Practice page 7 Name Date ft 16.4 ft Chapter 14 Skills Practice 935

16 936 Chapter 14 Skills Practice

17 Lesson 14.3 Skills Practice Name Date All Bubbly Volume of a Sphere Vocabulary Describe the similarities and differences between each term. 1. radius of a sphere and diameter of a sphere 2. diameter of a sphere and antipodes of a sphere 3. radius of a sphere and center of a sphere 4. hemisphere and sphere Chapter 14 Skills Practice 937

18 Lesson 14.3 Skills Practice page 2 Problem Set List the radius, diameter, distance of the center point to all other points on the sphere, and the approximate circumference. Use 3.14 for π m 6 in. Radius: 4 m Diameter: 8 m Center: 4 m from all points Circumference: 8π, or about m 938 Chapter 14 Skills Practice

19 Lesson 14.3 Skills Practice page 3 Name Date m 9 in. Chapter 14 Skills Practice 939

20 Lesson 14.3 Skills Practice page mm 3.25 ft Calculate the volume of each sphere. Use 3.14 for π. Round decimals to the nearest tenth, if necessary. 7. r 5 7 m 8. r 5 6 in. r = 7 m r = 6 in. V πr3 V π(7)3 V π V < m Chapter 14 Skills Practice

21 Lesson 14.3 Skills Practice page 5 Name Date 9. d 5 20 in. 10. d 5 16 m d = 20 in. d = 16 m 11. r cm 12. r mm r = 2.5 cm r = mm Chapter 14 Skills Practice 941

22 Lesson 14.3 Skills Practice page The radius of a sphere is 8 meters. 14. The radius of a sphere is 12 feet. 15. The diameter of a sphere is 20 centimeters. 16. The diameter of a sphere is 15 yards. Calculate the volume of the sphere using the radius, diameter, or circumference given. Use 3.14 for π. 17. The Atomium in Brussels, Belgium is a model of a unit cell of an iron crystal magnified 165 billion times. The model is made up of 8 steel spheres as vertices connected by tubes to form a cube shape with another sphere in the center. Each sphere of the Atomium is 18 meters in diameter. What is the volume of each sphere in the Atomium? V πr π(9)3 < 4 3 (3.14)(729) < The volume of each sphere of the Atomium is approximately cubic meters. 942 Chapter 14 Skills Practice

23 Lesson 14.3 Skills Practice page 7 Name Date 18. Spaceship Earth is the most recognizable structure at Epcot Center at Disney World in Orlando Florida. The ride is a geodesic sphere made up of thousands of small triangular panels. The circumference of Spaceship Earth is feet. What is its volume? 19. The Oriental Pearl Tower in Shanghai, China is a 468-meter high tower with 11 spheres along the tower. Two spheres are larger than the rest and house meeting areas, an observation deck, and a revolving restaurant. The lower of the two larger spheres has a radius of 25 meters and the higher sphere has a radius of 22.5 meters. What is the total volume of the two largest spheres on the Oriental Pearl Tower? Chapter 14 Skills Practice 943

24 Lesson 14.3 Skills Practice page The Globe Arena in Stockholm, Sweden is the world s largest hemispherical building. The diameter of the arena is 110 meters. The Globe Arena represents the sun in the world s largest scale model of the solar system. The Globe Arena is not a complete sphere, but if it were, what would its volume be? 21. A model of Earth is located 7600 meters from the Globe Arena in Sweden s solar system model. The circumference of the Earth model is centimeters. What is the volume of the Earth model? 944 Chapter 14 Skills Practice

25 Lesson 14.3 Skills Practice page 9 Name Date 22. The Montreal Biosphere is a geodesic dome that surrounds an environmental museum in Montreal, Canada. The dome has a radius of 125 feet. The structure is only 75% of a full sphere. What is its volume? Chapter 14 Skills Practice 945

26 946 Chapter 14 Skills Practice

27 Lesson 14.4 Skills Practice Name Date Practice Makes Perfect Volume Problems Problem Set Use the formulas for the volume of a cone, a sphere, and a cylinder to solve each problem. 1. Which paper cup can hold more and by how much: the cone or the cylinder? V 5 πr 1.5 in. 2 in. 2 h V πr2 h 3 in. 4.5 in. 5 π (1.5) 2 (3) π π(2)2 (4.5) 5 6π < in. 3 < in The cylindrical cup holds about cubic inches more than the conical cup. Chapter 14 Skills Practice 947

28 Lesson 14.4 Skills Practice page 2 2. Calculate the total volume of the Erlenmeyer flask. 4 cm 10 cm 20 cm 20 cm 948 Chapter 14 Skills Practice

29 Lesson 14.4 Skills Practice page 3 Name Date 3. The drinking glass is not a cylinder, but is actually part of a cone. Determine the volume of the glass. 4.5 cm 16 cm 3.5 cm 26 cm Chapter 14 Skills Practice 949

30 Lesson 14.4 Skills Practice page 4 4. A tennis ball company is designing a new can to hold 3 tennis balls. They want to waste as little space as possible. How much space does each can waste? Which can design should they choose? 2.75 in. 5.5 in in in in. 5.5 in. 950 Chapter 14 Skills Practice

31 Lesson 14.4 Skills Practice page 5 Name Date 5. A candle company makes pillar candles, spherical candles, and conical candles. They have an order for 3 pillar, 2 spherical, and 1 conical candle. Wax is sold in large rectangular blocks. What are the possible dimensions for a wax block that could be used to fill this order? 1.5 in. 5 in. 2 in. 4 in. 2.5 in. Chapter 14 Skills Practice 951

32 Lesson 14.4 Skills Practice page 6 6. A jeweler sold a string of fifty 8-millimeter pearls. He needs to choose a box to put them in. Which box should the jeweler choose? 10 mm 25 mm B 40 mm 15 mm A 952 Chapter 14 Skills Practice

33 Lesson 14.4 Skills Practice page 7 Name Date 7. An ice cream shop sells cones with a volume of 94.2 cubic centimeters. They want to double the volume of their cones without changing the diameter of the cone so the ice cream scoop will stay on top of the cone. What should the dimensions of the new cone be if the old cone had a height of 10 centimeters? Chapter 14 Skills Practice 953

34 Lesson 14.4 Skills Practice page 8 8. If you have a cylinder with a certain volume and you need another cylinder with the same volume but with double the radius, how should the height of the new cylinder relate to the height of the original cylinder? Give an example with measurements. 954 Chapter 14 Skills Practice