THANK YOU FOR YOUR PURCHASE!

Transcription

1 THANK YOU FOR YOUR PURCHASE! I hope that you find this resource helpful in your classroom. Please feel free to contact me with any questions as you implement this in your class. Maneuvering the Middle is an education blog with valuable tips for lesson planning, teacher organization, and math concepts in the middle school classroom. /ManeuveringTheMiddle maneuveringthemiddle.com PLEASE Print and copy this resource for your personal classroom use only. Save this to both home and school computers. Only post this only for students on a password protected class website. PLEASE DO NOT Reproduce or distribute this resource to other colleagues. Post this on the internet in any form, including classroom/personal websites, network drives, or other sharing websites (i.e. Amazon Inspire, etc). Maneuvering the Middle LLC, 2012-Present Products by Maneuvering the Middle, LLC may be used by the purchaser for their classroom use only. This is a single classroom license only. All rights reserved. If you wish to share this product with your team or colleagues, you may purchase additional licensing at a discounted rate. PAGE ONE

2 CLIPART AND FONT ATTRIBUTION Maneuvering the Middle resources include clipart and fonts from the following designers. MANEUVERINGTHEMIDDLE.COM PAGE TWO

3 Page Topic Resource 4 Sample Pacing Guide Volume Unit Table of Contents 5-6 Ideas for Implementation and Helpful Hints 7-15 Binder Covers, Dividers and Spine Labels Volume of Cylinders Student Handout Volume of Cylinders Homework Volume of Cones Student Handout 2 23 Volume of Cones Homework Applying Volume of Cylinders and Cones Student Handout 3 27 Volume of Cylinders and Cones Mini-Quiz Mini-Quiz Volume of Spheres Student Handout 4 31 Volume of Spheres Homework Applying Volume of Spheres Student Handout 5 35 Volume of Spheres Mini-Quiz Mini-Quiz Volume Study Guide CCSS Review CCSS Volume Study Guide Review Volume Unit Test Test Maneuvering the Middle LLC, 2016

4 Volume UNIT PAC ING GU I DE DAY 1 DAY 2 DAY 3 DAY 4 DAY 5 Volume of Cylinders Volume of Cones Applying Volume of Cylinders and Cones Volume of Spheres Applying Volume of Spheres Student Handout 1 Homework 1 Student Handout 2 Homework 2 Student Handout 3 Mini-Quiz 1 Student Handout 4 Homework 3 Student Handout 5 Mini-Quiz 2 DAY 6 DAY 7 notes Volume Study Guide Volume Test Study Guide Test Maneuvering the Middle LLC, 2017

5 VOLUME Student Handouts *NOTE: This file has been organized for double-sided printing. Any blank pages were left so intentionally to make printing easy. standards 8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Ideas for Implementation: This bundle has all of the notes, homework, quizzes, and tests to make your life easier and help your students to be successful with volume concepts. A sample pacing guide is included for those of you who do not have a district scope and sequence or if it is very general. Additionally, an answer key is included. If you notice any discrepancies in the documents or have any questions, please me at: support@maneuveringthemiddle.com. Maneuvering the Middle LLC, 2015

6 HELPFUL Hints Student Handouts A few ideas for organizing your curriculum and keeping things nice and neat. BINDERS Keep each unit in a separate binder. Use the spine labels and covers to keep them looking nice and easy to find. I personally love 1.5 inch binders. Page protectors I place my originals in page protectors in chronological order. I hole punch any extra copies from that lesson and place them behind that page. When I need an extra or a student is missing something from weeeeeeeeks ago, I can simply pull a copy out. Answer Keys I highlight the edges of my answer keys, or, if I am really good, I print them on colored paper. This helps them to stand out and makes them easy to find on my desk, in a binder, by the document camera, etc. Plus, highlighter doesn t show up if you make a copy. Cardstock Cardstock in a page protector makes an awesome divider. When I set up my dividers, I include one for each of the following: handouts, activities, assessments, and answer keys. Binder covers and spine labels have been included. Happy Teaching! Maneuvering the Middle LLC, 2015

7 Eighth Grade Curriculum volume Unit ten 8.g.9 MANEUVERING THE MIDDLE, 2016

8

9 volume volume volume Eighth Grade Curriculum U n i t t e n : 8. g. 9 Eighth Grade Curriculum U n i t t e n : 8. g. 9 Eighth Grade Curriculum U n i t t e n : 8. g. 9

10

11 Eighth Grade Curriculum volume Unit ten: Answer key MANEUVERING THE MIDDLE, 2016

12

13 Eighth Grade Curriculum volume Unit ten: activities MANEUVERING THE MIDDLE, 2016

14

15 Eighth Grade Curriculum volume Unit ten: assessments MANEUVERING THE MIDDLE, 2016

16

17 Unit: Volume Student Handout 1 Name Date Pd Volume of cylinders A cylindrical stack of coins is shown below. The dimensions of an individual coin are shown as well. If you needed to find the amount of space taken up by the stack of coins, how could you use the dimensions of the individual coin to help? 4 cm 1 cm VOLUME VOLUME OF CYLINDERS Volume is the amount of -dimensional occupied by an object. Volume can also be referred to as. To find the volume of a cylinder, multiply the of the base by the of the cylinder. The formula can be written as V = Bh. Describe each variable: V = B = h = The base of a cylinder will always be a, so to find the area of the base, use the formula. Find the volume of each cylinder. Use 3.14 for π in cm. 4 in. 8 cm. 2.5 ft. 10 ft. Formula: Formula: Formula: Plug in values: Plug in values: Plug in values: Volume: Volume: Volume: Maneuvering the Middle LLC, 2017

18 To leave an answer in terms of pi means to multiply everything except for, and simply leave the symbol in your solution. Find the volume of each cylinder below, both in terms of π and rounded to the nearest tenth mm in yd. 7 in mm. 1.5 yd. In terms of π: Nearest tenth: In terms of π: Nearest tenth: In terms of π: Nearest tenth: Use what you ve learned about the volume of cylinders to answer each question below. 7. The area of the base of a cylinder is 150 square inches. If the volume of the cylinder is 1,050 in. 3, what is the height of the cylinder? 8. The volume of a cylinder is 942 cubic feet. If the height of the cylinder is 12 feet, what is the radius of the cylinder? 9. Leann has a cylindrical water tank in her backyard that has a diameter of 3 meters and a height of 2 meters. What is the capacity of the water tank? 10. Drew and Beau both have cylindrical water bottles. Drew s water bottle has a diameter of 6 inches and a height of 7 inches. Beau s water bottle has a diameter of 4 inches and a height of 9 inches. Who s water bottle holds more water, and how much more water does it hold? Summarize today s lesson: Maneuvering the Middle LLC, 2017

19 Unit: Volume Homework 1 Name Date Pd Volume of cylinders Use your knowledge of the volume formula to solve the questions below. Show all work, and use 3.14 for ππ. 1. Which is the correct description of how to find the volume of a cylinder? A. Find the circumference of the base and multiply it by the height of the cylinder. B. Find the area of the base and multiply it by height of the cylinder. C. Square the area of the base and multiply it by the height of the cylinder. D. Find the area of the base and add it to the height of the cylinder. 2. Eric needs to find the area of the base of a cylinder. Which formula will help him? A. 2ππr B. 2ππrh C. ππr 2 D. 1 2 bh 4. Find the volume of the cylinder. Leave your answer in terms of ππ. 5 mm. 3. Mrs. Pitts wrote the volume formula as V=Bh. What does B represent? A. The radius of the base. B. The diameter of the base. C. The circumference of the base. D. The area of the base. 5. Find the volume of the cylinder. Leave your answer in terms of ππ. 8 cm. 8 cm mm. 6. The cylinder shown has a diameter of 11 inches. Find the volume of the cylinder. Round your solution to the nearest tenth. 7. The cylinder shown has a radius of 3 inches. The height is three times the radius. Find the volume of the cylinder. Round your solution to the nearest tenth. 4 in. Maneuvering the Middle LLC, 2017

20 8. A cylindrical basket has a volume of 15 cubic feet. If the height of the basket is 1.5 feet, what is the area of the base of the basket? 9. A container of candy is shaped like a cylinder and has a volume of cubic centimeters. If the height of the container is 10 centimeters, what is the radius of the container? 10. Jacob needs to know the volume of the cylinder shown. Which expression will give him the correct volume? 48 in. A. 3.14(48 2 )(2.5) B. 3.14(24 2 )(2.5) 2.5 ft. C. 3.14(2 2 )(2.5) D. 3.14(1 2 )(2.5) Maneuvering the Middle LLC, 2017

21 Unit: Volume Student Handout 2 Name Date Pd Volume of cones Example 1: Example 2: The cylinder and cone below have the same radius and the same height. The cylinder and cone below have the same radius and the same height. V = 120 in. 3 V = 40 in. 3 V = 90 in. 3 V = 30 in. 3 Using the examples above, what do you notice about the volume of a cone compared to the volume of a cylinder with the same radius and the same height? The volume of a cone will always be the volume of a cylinder with the same height and radius. Volume of cones The formula for the volume of a cone is, or. Since the base of a cone is a circle, the area of the base is found by using. Find the volume of each cone below. Use 3.14 for ππ r = 5 in. 12 in. 10 cm. d = 22 cm. Formula: Plug in values: Volume: Formula: Plug in values: Volume: Maneuvering the Middle LLC, 2016

22 3. The volume of several cylinders is shown below. (Note: cylinders are not drawn to scale.) A Use the dimensions in the table below to find the volume of each cone. Then, under the cylinder column, record the letter of the cylinder above that could have the same height and the same radius as the cone. Not all of the cylinders will be used. Dimensions of cone Volume of cone Cylinder Radius: 8 Height: 2 b c e u u u u u 3 d Diameter: 6 Height: 4 Radius: 2.5 Height: 2 Use your knowledge of the formula for volumes of cones to answer the questions below. 4. The cone below has a diameter of 12 units and a slant height of 10 units. Find the volume of the cone. 5. Isabella constructed a cylindrical vase that has a volume of 63 cubic centimeters. Jason constructed a cone that had the same height and the same radius as Isabella s cylinder. What is the volume of Jason s cone? 6. A cone has a volume of 300 units 3, and a cylinder has a volume of 100 units 3. Is it possible that the cylinder and the cone have the same height and the same radius? Why or why not? 7. A cone has a volume of 942 cubic inches and a height of 9 inches. What is the radius of the cone? Summarize today s lesson: Maneuvering the Middle LLC, 2016

23 Unit: Volume Homework 2 Name Date Pd Volume of cones Find the volume of each cone. Use 3.14 for ππ and round answers to the nearest tenth. Match each answer to a letter below to help you solve the riddle d = d = r = r = 9 d = 4 r = d = 30 r = r = 1.5 g u 3 d u 3 O 623 u 3 e 4,220.2 u 3 s 718 u 3 h u 3 t u 3 e 7.1 u 3 a 25.1 u 3 U 21.3 u 3 p u 3 i 8,007 u 3 Why would a prism beat a sphere in a competition? Maneuvering the Middle LLC, 2016

24

25 Unit: Volume Student Handout 3 Name Date Pd Applying volume of cylinders and cones Use the formulas for the volume of cylinders and cones to help you solve the problems below. Use 3.14 for ππ. 1. Victoria bought coffee in a cup shaped like a cylinder with a radius of 5 centimeters and a height of 15 centimeters. Victoria fills the cup with coffee, but she leaves 4.5 centimeters of space at the top to have room for cream. What is the volume of coffee in her cup? I know: I need to know: plan and work: My Solution: 2. A tea vendor gives samples of tea in cone shaped cups. The cups have a diameter of 4 inches and a height of 5 inches. If there are about 0.55 fluid ounces in one cubic inch, how many fluid ounces of tea will one sample cup hold? Round to the nearest tenth. I know: I need to know: plan and work: My Solution: Maneuvering the Middle LLC, 2017

26 In a group, take turns rolling a number cube. After rolling a number, read the corresponding problem below and lead your group in solving the question. 1. Dennis has three identical cylinders filled with water. How many cones should he be able to fill with the water if the cones have the same radius and the same height as the cylinders? Explain. 2. A cone has a volume 7,065 in. 3 and a height of 30 inches. What is the radius of the cone? 3. A cylindrical cooler has a diameter of 30 inches and a height of 24 inches. Runners in a marathon can use cone shaped cups to get a drink from the cooler. If the cups have a diameter of 3 inches and a height of 4 inches, how many full cups would be able to be filled from the cooler? 4. A cone has a slant height of 26 inches and a diameter of 48 inches. What is the volume of the cone? 5. Tess gets a snow cone in a cone shaped container. The container has a diameter of 3 inches and a height of 5 inches. If the snow cone costs $0.20 per cubic inch, how much would her snow cone cost if the container is filled to the top? 6. A swimming pool is shaped like a cylinder with a radius of 15 feet and a height of 6 feet. If one cubic foot holds 7.48 gallons of water, how many gallons of water can the swimming pool hold? Summarize today s lesson: Maneuvering the Middle LLC, 2017

27 Unit: Volume Mini-Quiz 1 1. Find the volume of the cone. Name Date Pd Volume of cylinders and cones mini-quiz Solve each of the problems below, and use 3.14 for ππ. 2. Find the volume of the cylinder. 3.5 ft. 3. Find the volume of the cone. 9 cm. r = 2 ft. d = 8 in. 12 in. r = 6 cm. 4. A cylinder has a volume of 198 cm 3, and its base has an area of 22 cm 2. What is the height of the cylinder? 5. A cone has a volume of 33 cubic inches. If a cylinder has the same height and the same radius as the cone, what is the volume of the cylinder? Maneuvering the Middle LLC, 2016 Unit: Volume Mini-Quiz 1 1. Find the volume of the cone. Name Date Pd Volume of cylinders and cones mini-quiz Solve each of the problems below, and use 3.14 for ππ. 2. Find the volume of the cylinder. 3.5 ft. 3. Find the volume of the cone. 9 cm. r = 2 ft. d = 8 in. 12 in. r = 6 cm. 4. A cylinder has a volume of 198 cm 3, and its base has an area of 22 cm 2. What is the height of the cylinder? 5. A cone has a volume of 33 cubic inches. If a cylinder has the same height and the same radius as the cone, what is the volume of the cylinder? Maneuvering the Middle LLC, 2016

28

29 Unit: Volume Student Handout 4 VOLUME OF SPHERES Volume of spheres Name Date Pd The volume of a sphere can be found by using the formula. Half of a sphere is called a. If a cylinder and a sphere have the same radius and the same height (the height of the sphere would be ), then the sphere will have the volume of the cylinder. Use this fact to help you see how the formula for the volume of spheres was derived in the table below. 1. Formula for volume of a cylinder ππr 2 h 2. Replace h with 2r ππr 2 (2r) 3. Multiply the formula by Simplify 2 3 ππr2 (2r) 4 3 ππr3 Find the volume of each sphere and use 3.14 for ππ r = 3 d = 12 r = 5 Formula: Plug in values: Volume: Formula: Plug in values: Volume: Formula: Plug in values: Volume: Maneuvering the Middle LLC, 2017

30 In 4-6, find the volume of each sphere, and leave your solutions in terms of ππ d = 13 r = 12 r = 9.3 Formula: Plug in values: Volume: Formula: Plug in values: Volume: Formula: Plug in values: Volume: Use the formula for the volume of spheres to help you answer each question below. 7. A hemisphere has a radius of 7 inches. Find the volume of the hemisphere. 8. A sphere has a volume of 288ππ in 3. Find the radius of the sphere. 9. A sphere has a volume of 972ππ in 3. Find the radius of the sphere. 10. A cylinder, a cone and a sphere all have a radius of 3 feet and a height of 6 feet. Find the volume of each and record it in the table. CYLINDER CONE SPHERE a. What is the ratio of the volume of the sphere to the volume of the cylinder? b. How does the volume of the sphere compare to the cone? c. List the figures in order of the greatest capacity to the least capacity. Summarize today s lesson: Maneuvering the Middle LLC, 2017

31 Unit: Volume Homework 3 Name Date Pd Part I: Draw a line connecting each sphere to its volume in terms ofπ and rounded to the nearest tenth. (Not all of the values will be used.) 1. SPHERE VOLUME (IN TERMS OF PI) VOLUME (NEAREST TENTH) d = 9 Volume of spheres π units 3 3,052.1 units 3 2. r = π units 3 67 units π units units 3 3. d = π units units 3 4. r = 9 972π units 3 10,052.2 units 3 3,201. 3π units 3 1,436 units 3 Part II: Answer each question below. 5. Find the volume of a hemisphere that has a radius of 8 centimeters. Round to the nearest tenth. 6. Find the volume of a hemisphere that has a diameter of 48 inches. Leave your answer in terms of ππ. 7. A sphere has a volume of 36ππ in 3. Find the radius of the sphere. 8. A sphere has a volume of 2,304ππ mm 3. Find the diameter of the sphere. Maneuvering the Middle LLC, 2017

32

33 Unit: Volume Student Handout 5 Name Date Pd Applying volume of spheres Use the formula for the volume of spheres to help you solve the problems below. Use 3.14 for ππ. 1. A stadium is shaped like a hemisphere with a radius of 150 feet. Last month, the owners of the stadium paid $0.05 per cubic foot to cover the cost of utilities. What was the total cost for utilities last month? I know: I need to know: plan and work: My Solution: 2. A sphere has a radius of 3 inches. A cylinder has a radius of 3 inches and a height of 6 inches. If the sphere is filled with water and is poured into the cylinder, what will the height of water in the cylinder be? I know: I need to know: plan and work: My Solution: Maneuvering the Middle LLC, 2016

34 3. Jasmine is decorating her Christmas tree with ornaments shaped like spheres. There are 35 ornaments total and each has a radius of 3 inches. If the ornaments are filled with glitter, how many total cubic inches of glitter are contained in the ornaments? I know: I need to know: plan and work: My Solution: 4. Hugo has a cylindrical container that holds marbles. The container has a height of 10 inches and radius of 5 inches. Each marble is shaped like a sphere with a radius of 1 inch. If there are 150 marbles in the container, how much empty space is in the container? I know: I need to know: plan and work: My Solution: 5. A sphere has a volume of 150 cubic inches. Find the volume of a cylinder and a cone that both have the same radius and the same height as the sphere. I know: I need to know: plan and work: My Solution: Summarize today s lesson: Maneuvering the Middle LLC, 2017

35 Unit: Volume Mini-Quiz 2 In the problems below, use 3.14 for ππ. 1. Find the volume of the sphere. Leave your answer in terms of ππ. r = 4 d = 18 Volume of spheres mini-quiz 2. Find the volume of the sphere. Name Date Pd 3. Find the volume of a hemisphere with a radius of 11 inches. Round to the nearest tenth. 4. A sphere has a volume of 4,500ππ cubic feet. Find the radius of the sphere. 5. Skylar has pool toys shaped like a sphere with a radius of 2 inches. The toys fill with water, and she has 12 toys total. How many cubic inches of water would it take to fill all 12 toys with water? Maneuvering the Middle LLC, 2016 Unit: Volume Mini-Quiz 2 In the problems below, use 3.14 for ππ. 1. Find the volume of the sphere. Leave your answer in terms of ππ. r = 4 d = 18 Volume of spheres mini-quiz 2. Find the volume of the sphere. Name Date Pd 3. Find the volume of a hemisphere with a radius of 11 inches. Round to the nearest tenth. 4. A sphere has a volume of 4,500ππ cubic feet. Find the radius of the sphere. 5. Skylar has pool toys shaped like a sphere with a radius of 2 inches. The toys fill with water, and she has 12 toys total. How many cubic inches of water would it take to fill all 12 toys with water? Maneuvering the Middle LLC, 2016

36

37 Unit: Volume Review CCSS Name Date Pd Volume Study guide Solve each of the problems below using 3.14 for π. Be sure to ask questions if you need more help with a topic. I can use a formula to find the volume of cylinders. 1. What is the formula used to find the volume of a cylinder? Describe the steps to finding the volume of a cylinder in your own words. 8.g.9 2. Find the volume of the cylinder. Leave your answer in terms of ππ. 8 mm. 3. Find the volume of the cylinder. Round to the nearest tenth. 15 in. 4. A cylindrical can has a radius of 5.5 cm and a height of 8 cm. What is the capacity of the can? 24 mm. 11 in. I can use a formula to find the volume of cones. 5. Laura is trying to find the volume of a cone. So far she has found the area of the base of the cone and multiplied it by the height of the cone. Describe what she needs to do next. 6. A cylinder has a volume of 72 cubic inches. What is the volume of a cone with the same height and radius as the cylinder? Explain. 8.g.9 7. Find the volume of the cone. Leave your answer in terms of ππ Find the volume of the cone. Round to the nearest tenth. r = 2.5 in. 7 in. 9. A cone has a diameter of 18 units and a slant height of 15 units. Find the volume of the cone. d = 36 Maneuvering the Middle LLC, 2016

38 I can use a formula to find the volume of spheres. 10. Find the volume of the sphere. Round to the nearest tenth. d = 22 8.g A sphere shaped snow globe has a radius of 3.5 inches. How much water can the snow globe hold? Round to the nearest tenth. 12. A cylinder has a volume of 75 cubic centimeters. What is the volume of a sphere with the same radius and height as the cylinder? Explain. 13. Find the volume of a hemisphere with a radius of 7 inches. Round to the nearest tenth. The questions below give a description of a sphere. Match each description with the volume of the sphere in terms of ππ. A. 972ππ 14. A sphere with a radius of 18 units B. 7,776ππ 15. A sphere with a diameter of 24 units C. 1,230ππ 16. A sphere with a diameter of 18 units D. 4,500ππ 17. A sphere with a radius of 15 units E. 2,304ππ I can use formulas for volume to solve mathematical problems. 18. A cone shaped funnel can hold 314 cubic inches of water. If the height of the funnel is 12 inches, what is the radius of the funnel? 8.g A cylindrical vase is filled with soil. If the height of the vase is 6 centimeters and the vase holds 471 cubic centimeters, what is the diameter of the vase? 20. The volume of a sphere is 36,000ππ units 3. What is the radius of the sphere? 21. The volume of a cylinder is 300 feet 3. Find the volume of a cone and a sphere that have the same height and radius as the cylinder. Cone: Sphere: Maneuvering the Middle LLC, 2016

39 I can use formulas for volume to solve real-world problems. 22. The radius of a basketball is 10 inches, and the radius of a soccer ball is 9 inches. How much greater is the volume of the basketball than the soccer ball? Round to the nearest tenth Derek has a cylindrical water bottle with a diameter of 4 centimeters and a height of 15 8.g.9 centimeters. If he filled the water bottle 3 4 full of water, how much water is in the water bottle? 24. At a wedding, guests have cone shaped containers that hold flower petals to throw on the bride and groom as they leave. The cones have a radius of 5 centimeters and a height of 10 centimeters. If there are 150 cones, what is the total volume that all of the cones will hold? 25. A cylindrical cooler is filled with juice. The container has a radius of 7 inches and a height of 18 inches. If a cubic inch contains about.004 gallons of juice, how many gallons of juice does the container hold? Round to the nearest tenth. 26. A cylindrical tank with a radius of 12 inches and a height of 20 inches is full of water. Does the tank have enough water to fill 250 spherical shaped water balloons if each of the water balloons has a radius of 2 inches? Explain. I can use the formulas for volume to solve mathematical problems. Match each description of a figure with the formula that would be used to find its volume. 8.g A sphere with a radius of A cylinder with a diameter of 8 and a height of A cone with a radius of 8 and a height of A sphere with a diameter of 8 A. 3.14(4 2 )(2) B. ( 4 3 )(3.14)(43 ) C. ( 1 3 )(3.14)(82 )(2) D. ( 1 3 )(3.14)(43 ) E. ( 4 3 )(3.14)(83 ) Maneuvering the Middle LLC, 2016

40

41 Unit: Volume Review Name Date Pd Volume Study guide Solve each of the problems below using 3.14 for π. Be sure to ask questions if you need more help with a topic. I can use a formula to find the volume of cylinders. 1. What is the formula used to find the volume of a cylinder? Describe the steps to finding the volume of a cylinder in your own words. 2. Find the volume of the cylinder. Leave your answer in terms of ππ. 8 mm. 3. Find the volume of the cylinder. Round to the nearest tenth. 15 in. 4. A cylindrical can has a radius of 5.5 cm and a height of 8 cm. What is the capacity of the can? 24 mm. 11 in. I can use a formula to find the volume of cones. 5. Laura is trying to find the volume of a cone. So far she has found the area of the base of the cone and multiplied it by the height of the cone. Describe what she needs to do next. 6. A cylinder has a volume of 72 cubic inches. What is the volume of a cone with the same height and radius as the cylinder? Explain. 7. Find the volume of the cone. Leave your answer in terms of ππ Find the volume of the cone. Round to the nearest tenth. r = 2.5 in. 7 in. 9. A cone has a diameter of 18 units and a slant height of 15 units. Find the volume of the cone. d = 36 Maneuvering the Middle LLC, 2016

42 I can use a formula to find the volume of spheres. 10. Find the volume of the sphere. Round to the nearest tenth. d = A sphere shaped snow globe has a radius of 3.5 inches. How much water can the snow globe hold? Round to the nearest tenth. 12. A cylinder has a volume of 75 cubic centimeters. What is the volume of a sphere with the same radius and height as the cylinder? Explain. 13. Find the volume of a hemisphere with a radius of 7 inches. Round to the nearest tenth. The questions below give a description of a sphere. Match each description with the volume of the sphere in terms of ππ. A. 972ππ 14. A sphere with a radius of 18 units B. 7,776ππ 15. A sphere with a diameter of 24 units C. 1,230ππ 16. A sphere with a diameter of 18 units D. 4,500ππ 17. A sphere with a radius of 15 units E. 2,304ππ I can use formulas for volume to solve mathematical problems. 18. A cone shaped funnel can hold 314 cubic inches of water. If the height of the funnel is 12 inches, what is the radius of the funnel? 19. A cylindrical vase is filled with soil. If the height of the vase is 6 centimeters and the vase holds 471 cubic centimeters, what is the diameter of the vase? 20. The volume of a sphere is 36,000ππ units 3. What is the radius of the sphere? 21. The volume of a cylinder is 300 feet 3. Find the volume of a cone and a sphere that have the same height and radius as the cylinder. Cone: Sphere: Maneuvering the Middle LLC, 2016

43 I can use formulas for volume to solve real-world problems. 22. The radius of a basketball is 10 inches, and the radius of a soccer ball is 9 inches. How much greater is the volume of the basketball than the soccer ball? Round to the nearest tenth Derek has a cylindrical water bottle with a diameter of 4 centimeters and a height of 15 centimeters. If he filled the water bottle 3 4 full of water, how much water is in the water bottle? 24. At a wedding, guests have cone shaped containers that hold flower petals to throw on the bride and groom as they leave. The cones have a radius of 5 centimeters and a height of 10 centimeters. If there are 150 cones, what is the total volume that all of the cones will hold? 25. A cylindrical cooler is filled with juice. The container has a radius of 7 inches and a height of 18 inches. If a cubic inch contains about.004 gallons of juice, how many gallons of juice does the container hold? Round to the nearest tenth. 26. A cylindrical tank with a radius of 12 inches and a height of 20 inches is full of water. Does the tank have enough water to fill 250 spherical shaped water balloons if each of the water balloons has a radius of 2 inches? Explain. I can use the formulas for volume to solve mathematical problems. Match each description of a figure with the formula that would be used to find its volume. 27. A sphere with a radius of A cylinder with a diameter of 8 and a height of A cone with a radius of 8 and a height of A sphere with a diameter of 8 A. 3.14(4 2 )(2) B. ( 4 3 )(3.14)(43 ) C. ( 1 3 )(3.14)(82 )(2) D. ( 1 3 )(3.14)(43 ) E. ( 4 3 )(3.14)(83 ) Maneuvering the Middle LLC, 2016

44

45 Unit: Volume Test Solve the problems below. Use 3.14 for ππ, and be sure to show all work. 1. What is the volume of the cylinder below? 10 in. Volume unit test Name Date Pd 2. Angela needs to find the volume of the sphere shown below. Which formula should she use? A. 4 3 (ππ)(173 ) 30 in. d = 17 B. 4 3 (ππ)(172 ) C. 4 3 (ππ)(8.53 ) 3. Jessie is looking for the volume of the cone below, and she is using the formula V = ( 1 3 )Bh. Which of the following is the value of B? A units 2 B. 1, units 2 C units 2 D. 36 units 2 5. Ollie has a jar of preserves in the shape of the cylinder shown below. If the jar is currently 1 4 full of preserves, what is the volume of preserves in the jar? A units 3 B units 3 C units 3 D units in. r = 6 8 in. 4. What is the volume of the cone shown below? Round to the nearest tenth. d = 2 ft. 6. Which of the following is the volume of a hemisphere with a radius of 8 inches? A. 1, inches 3 B. 1, inches 3 C. 2, inches 3 D inches 3 D. 4 3 (ππ)(8.52 ) 5 ft. 7. The cone shown below has a slant height of 15 centimeters and a height of 12 centimeters. a. What is the radius of the cone? b. What is the volume of the cone? Maneuvering the Middle LLC, 2016

46 Solve the problems below. Use 3.14 for ππ, and be sure to show all work. 8. Find the volume of the sphere shown below. Leave your answer in terms of ππ. 9. A kid s pool is cylindrical and has a radius of 5 feet and a height of 2 feet. If a cubic foot holds about 7.48 gallons of water, how many gallons of water does the kid s pool hold? r = A cylinder has a volume of 24 cubic feet. Which of the following could have the same radius and height as the cylinder? A. A cone with a volume of 72 ft. 3 B. A cone with a volume of 32 ft. 3 C. A sphere with a volume of 18 ft. 3 D. A cone with a volume of 8 ft. 3 A. 157 gallons B gallons C. 1,174.4 gallons D. 21 gallons 11. A frozen yogurt shop allows guests to fill a cone shaped cup with frozen yogurt, and customers pay $0.08 per cubic inch. If each cup has a radius of 3 inches and a height of 5 inches, what would it cost to fill the cone to it s full capacity? A. $3.77 B. $1.88 C. $11.30 D. $ A cone, a cylinder and a sphere all have the same radius and the same height. Which would have the largest volume? A. The cone B. The cylinder C. The sphere D. The sphere and the cylinder would have the same volume. 14. The cylinder below has a volume of 2,512 cm 3 and a height of 8 centimeters. What is the diameter of the cylinder? 13. Harvey bought two pi natas, one shaped like a soccer ball and one shaped like a basketball. Both pi natas are spheres with a radius of 5 inches. What is the total volume of both pi natas? Round to the nearest tenth. 15. Darla has three buckets shaped like cylinders. She is filling the buckets with water by using a scoop shaped like a cone. If the cone has the same radius and the same height as the buckets, how many scoops will it take her to fill the three buckets? A. 3 scoops B. 9 scoops C. 27 scoops D. There is not enough information to tell. Maneuvering the Middle LLC, 2016