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Go Math Grade 8 Answer Key Chapter 13 Volume
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Go Math Grade 8 Chapter 13 Volume Answer Key
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Lesson 1: Volume of Cylinders
- Volume of Cylinders – Page No. 402
- Volume of Cylinders – Page No. 403
- Volume of Cylinders – Page No. 404
Lesson 2: Volume of Cones
- Volume of Cones – Page No. 408
- Volume of Cones – Page No. 409
- Volume of Cones – Page No. 410
Lesson 3: Volume of Spheres
- Volume of Spheres – Page No. 414
- Volume of Spheres – Page No. 415
- Volume of Spheres – Page No. 416
Model Quiz :
- Model Quiz – Page No. 417
- Mixed Review – Page No. 418
Guided Practice – Volume of Cylinders – Page No. 402
Question 1. Vocabulary Describe the bases of a cylinder. Type below: ____________
Answer: The ends of a cylinder are the bases of the cylinder of the two flat surfaces.
![lesson 1 problem solving practice volume of cylinders answer key Go Math Grade 8 Answer Key Chapter 13 Volume Lesson 1: Volume of Cylinders img 1](https://i0.wp.com/gomathanswerkey.com/wp-content/uploads/2020/08/Go-Math-Grade-8-Answer-Key-Chapter-13-Volume-img-1.jpg?resize=217%2C181&ssl=1)
Explanation: Number of inch cubes that fit in the base of the cylinder = 61 Number of inch cubes that fit in the length of the cylinder = 7 The volume of cylinder = base area x height V= 61 x 7 V = 427 cubic units. Volume of each cube = 1 in³ Volume of cylinder = 427in³
![lesson 1 problem solving practice volume of cylinders answer key Go Math Grade 8 Answer Key Chapter 13 Volume Lesson 1: Volume of Cylinders img 2](https://i0.wp.com/gomathanswerkey.com/wp-content/uploads/2020/08/Go-Math-Grade-8-Answer-Key-Chapter-13-Volume-img-2.jpg?resize=498%2C194&ssl=1)
Answer: The volume of the cylinder is approximately 1695.6 m 3 . 1695.6m³
Explanation: V = πr²h V = π . 6² . 15 V = 3.14 × 36 × 15 V = 1695.6m³
Question 4. A Japanese odaiko is a very large drum that is made by hollowing out a section of a tree trunk. A museum in Takayama City has three odaikos of similar size carved from a single tree trunk. The largest measures about 2.7 meters in both diameter and length, and weighs about 4.5 metric tons. Using the volume formula for a cylinder, approximate the volume of the drum to the nearest tenth. The radius of the drum is about _____ m. The volume of the drum is about _____ m 3 . The radius of the drum is about ___________ m The volume of the drum is about ___________ m 3
Answer: The radius of the drum is about 1.35 m. The volume of the drum is about 15.5 m 3 .
Explanation: Diameter of base of drum = 2.7 m The radius of the base of the drum = 2.7/2 R = 1.35 m The volume of cylinder = πr²h Height (h) = 2.7 m Radius (R) = 1.35 m Volume = 3.14 × (1.35) × 2.7 V = 15.4511 m³ V = 15.5 m³
ESSENTIAL QUESTION CHECK-IN
Question 5. How do you find the volume of a cylinder? Describe which measurements of a cylinder you need to know. Type below: ____________
Answer: The volume of the cylinder is = πr²h
Explanation: We need to find the radius of the base, r, and the height of the cylinder, h. The volume of the cylinder is = πr²h
13.1 Independent Practice – Volume of Cylinders – Page No. 403
Find the volume of each figure. Round your answers to the nearest tenth if necessary. Use 3.14 for π.
![lesson 1 problem solving practice volume of cylinders answer key Go Math Grade 8 Answer Key Chapter 13 Volume Lesson 1: Volume of Cylinders img 3](https://i0.wp.com/gomathanswerkey.com/wp-content/uploads/2020/08/Go-Math-Grade-8-Answer-Key-Chapter-13-Volume-img-3.jpg?resize=289%2C83&ssl=1)
Answer: 569.9 cm³
Explanation: Radius of base = 11 cm Height of cylinder = 1.5 cm The volume of the cylinder = πr²h V = 3.14 × (11)² × 1.5 V = 569.91 V = 569.9 cm³
![lesson 1 problem solving practice volume of cylinders answer key Go Math Grade 8 Answer Key Chapter 13 Volume Lesson 1: Volume of Cylinders img 4](https://i0.wp.com/gomathanswerkey.com/wp-content/uploads/2020/08/Go-Math-Grade-8-Answer-Key-Chapter-13-Volume-img-4.jpg?resize=222%2C88&ssl=1)
Answer: 1205.8 in³
Explanation: Radius of base = 4 in Height of cylinder = 24 in The volume of cylinder = πr²h V = 3.14 × (4)² × 24 V = 1205.76 V = 1205.8 in³
![lesson 1 problem solving practice volume of cylinders answer key Go Math Grade 8 Answer Key Chapter 13 Volume Lesson 1: Volume of Cylinders img 5](https://i0.wp.com/gomathanswerkey.com/wp-content/uploads/2020/08/Go-Math-Grade-8-Answer-Key-Chapter-13-Volume-img-5.jpg?resize=193%2C102&ssl=1)
Answer: 1256 m³
Explanation: Radius of base = 5 m Height of cylinder = 16 m The volume of the cylinder = πr²h V = 3.14 × (5)² × 16 V = 1256 V = 1256 m³
![lesson 1 problem solving practice volume of cylinders answer key Go Math Grade 8 Answer Key Chapter 13 Volume Lesson 1: Volume of Cylinders img 6](https://i0.wp.com/gomathanswerkey.com/wp-content/uploads/2020/08/Go-Math-Grade-8-Answer-Key-Chapter-13-Volume-img-6.jpg?resize=130%2C125&ssl=1)
Answer: 942 in³
Explanation: Diameter of base = 10 in Radius of base = 5 in Height of cylinder = 12 in The volume of the cylinder = πr²h V = 3.14 × (5)² × 12 V = 942 in³
Question 10. A cylinder has a radius of 4 centimeters and a height of 40 centimeters. _________ cm 3
Answer: 2009.6 cm³
Explanation: Radius of base = 4 cm Height of cylinder = 40 cm The volume of cylinder = πr²h V = 3.14 × (4)² × 40 V = 2009.6 cm³
Question 11. A cylinder has a radius of 8 meters and a height of 4 meters. _________ m 3
Answer: 803.8 m³
Explanation: The radius of base = 8 m Height of cylinder = 4 m The volume of the cylinder = πr²h V = 3.14 × (8)² × 4 V = 803.84 m³ V = 803.8 m³
Round your answer to the nearest tenth, if necessary. Use 3.14 for π.
Question 12. The cylindrical Giant Ocean Tank at the New England Aquarium in Boston is 24 feet deep and has a radius of 18.8 feet. Find the volume of the tank. _________ ft 3
Answer: 26635.2 ft³
Explanation: The base radius of the tank = 18.8 ft Depth of the tank in the ocean = 24 ft The volume of the cylinder = πr²h V = 3.14 × (18.8)² × 24 V = 3.14 × 354.44 × 24 V = 26635.2384 ft³ V = 26635.2 ft³
Question 13. A standard-size bass drum has a diameter of 22 inches and is 18 inches deep. Find the volume of this drum. _________ in 3
Answer: 6838.9 in³
Explanation: The base diameter of the drum = 22 in Base radius of the drum = 22/2 = 11 in Depth of the bass drum = 18 in The volume of the bass drum = πr²h V = 3.14 × (11)² × 18 V = 3.14 × 121 × 18 V = 6838.92 in³ V = 6838.9 in³
Question 14. Grain is stored in cylindrical structures called silos. Find the volume of a silo with a diameter of 11.1 feet and a height of 20 feet. _________ ft 3
Answer: 1934.4 ft³
Explanation: Base diameter of silo = 11.1 ft Base radius of the silo = 11.1/2 = 5.55 ft Depth of the silo = 20 ft Volume of the silo = πr²h V = 3.14 × (5.55)² × 18 V = 3.14 × 30.8025 × 18 V = 1934.397 ft³ V = 1934.4 ft³
Question 15. The Frank Erwin Center, or “The Drum,” at the University of Texas in Austin can be approximated by a cylinder that is 120 meters in diameter and 30 meters in height. Find its volume. _________ m 3
Answer: 339120 m³
Explanation: Base diameter of the drum = 120 m Base radius of the drum = 120/2 = 60 m Height of the drum = 30 m Volume of the drum = πr²h V = 3.14 × (60)² × 30 V = 3.14 × 3600 × 30 V = 339120 m³
Volume of Cylinders – Page No. 404
Question 16. A barrel of crude oil contains about 5.61 cubic feet of oil. How many barrels of oil are contained in 1 mile (5280 feet) of a pipeline that has an inside 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? __________ barrels $ __________
Answer: 184.7 barrels $18470
Explanation: Volume of barrel = 5.61 cubic feet Length of the pipe = 1 mile = 5280 feet Diameter of the pipe = 6 inches = 0.5 feet Radius of the pipe = 6/2 inches = 3 inches = 0.25 feet Volume of oil in the pipe = πr²h = 3.14 × (0.25)² × 5280 = 1036.2 cubic feet Number of barrels in the pipe = 1036.2/5.61 = 184.7 barrels Cost of one barrel = $100 Cost of 184.7 barrels =184.7 × $100 = $18470
![lesson 1 problem solving practice volume of cylinders answer key Go Math Grade 8 Answer Key Chapter 13 Volume Lesson 1: Volume of Cylinders img 7](https://i0.wp.com/gomathanswerkey.com/wp-content/uploads/2020/08/Go-Math-Grade-8-Answer-Key-Chapter-13-Volume-img-7.jpg?resize=195%2C174&ssl=1)
Answer: 57.697 in³
Explanation: The length of the pan = 12 in The diameter of the pan = 3.5 in Radius = 3.5/2 = 1.75 in The volume of uncooked dough = Half the volume of the full cylinder of the above dimensions. = (πr²h)/2 = (3.14 × (1.75)² × 12)/2 = 115.395/2 = 57.697 in³
FOCUS ON HIGHER ORDER THINKING
Question 18. Explain the Error A student said the volume of a cylinder with a 3-inch diameter is two times the volume of a cylinder with the same height and a 1.5-inch radius. What is the error? Type below: _______________
Answer: The volume of the cylinder of 3 in is four times the volume of the new cylinder of radius 1.5 in
Explanation: The volume of a cylinder is directly proportional to the square of the radius of the cylinder. The volume does not depend on the radius linearly. Volume = πr²h V1 = π(3)²h V2 = π(1.5)²h V1/V2 = (π(3)²h)/(π(1.5)²h) V1/V2 = 4 V1 = 4V2
Volume of Cylinders and Cones Mini Quiz Answer Key Question 19. Communicate Mathematical Ideas Explain how you can find the height of a cylinder if you know the diameter and the volume. Include an example with your explanation. Type below: _______________
Answer: Let the diameter be D. Radius r = D/2 Volume = πr²h Volume = π(D/2)²h V = π((D)²/4)h h = 4V/π(D)² To find the height of a cylinder with diameter D = 2 m Let the volume be 10 m³ h = 4V/π(D)² h = (4 × 10)/(3.14 × 2²) h = 3.18 m³
Question 20. 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. Fraction: \(\frac{□}{□}\)
Answer: \(\frac{VA}{4}\)
Explanation: rA = 6 cm rB = half of the radius of cylinder A = 3 cm hA = hB VA = πrA²h VB = πrB²h VA/VB = (πrA²h)/(πrB²h) VA/VB = 6²/3² = 36/9 = 4 Thus VB = VA/4
Guided Practice – Volume of Cones – Page No. 408
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Answer: 150 in³
Explanation: In the question, the area of the base of the cylinder, B = 45 in² Height of the cylinder, h = 10 inch Volume of the cylinder, V cylinder = B × h = 45 × 10 = 450 inch³ Volume of the cone, V Cone = 1/3 V cylinder =1/3(450 inch) = 150 inch³ So, the volume of the cone is Vcone = 150 in³
Volume of Cylinders and Cones Mini Quiz Answer Key Question 2. A cone and a cylinder have congruent heights and bases. The volume of the cone is 18 m 3 . What is the volume of the cylinder? Explain. _________ m 3
Answer: 54 m 3
Explanation: The volume of the cone is 18 m 3 . Vcone = 1/3 Vcylinder Vcylinder = 3Vcone Vcylinder = 3.18 Vcylinder = 54 m 3
Find the volume of each cone. Round your answer to the nearest tenth if necessary. Use 3.14 for π.
![lesson 1 problem solving practice volume of cylinders answer key Go Math Grade 8 Answer Key Chapter 13 Volume Lesson 2: Volume of Cones img 9](https://i0.wp.com/gomathanswerkey.com/wp-content/uploads/2020/08/Go-Math-Grade-8-Answer-Key-Chapter-13-Volume-img-9.jpg?resize=144%2C177&ssl=1)
Answer: 65.94 ft³
Explanation: the diameter of the cone is 6ft. so, the radius of the cone is 3ft. the height of the cone is 7ft. the volume of the cone = 1/3 × πr²h = 1/3 × 3.14 × 3² × 7 = 65.94 ft³
![lesson 1 problem solving practice volume of cylinders answer key Go Math Grade 8 Answer Key Chapter 13 Volume Lesson 2: Volume of Cones img 10](https://i0.wp.com/gomathanswerkey.com/wp-content/uploads/2020/08/Go-Math-Grade-8-Answer-Key-Chapter-13-Volume-img-10.jpg?resize=124%2C149&ssl=1)
Answer: 113982in³
Explanation: The radius is 33inch and the height is 100 inch Volume of the cone = 1/3 × πr²h = 1/3 × π(33)²100 = 113982in³
Question 5. Gretchen made a paper cone to hold a gift for a friend. The paper cone was 15 inches high and had a radius of 3 inches. Find the volume of the paper cone to the nearest tenth. Use 3.14 for π. _________ in 3
Answer: 141.3in³
Explanation: the radius of the cone is 3inch and the height of the cone is 15inch. Volume of the cone = 1/3 × πr²h = 1/3 × π(3)² × 15 = 141.3in³
Question 6. A cone-shaped building is commonly used to store sand. What would be the volume of a cone-shaped building with a diameter of 50 meters and a height of 20 meters? Round your answer to the nearest tenth. Use 3.14 for π. _________ m 3
Answer: 13083.33 m³
Explanation: The diameter of the cone is 50 meters. So, the radius of the cone is 25 meters. The height of the cone is 20 meters. Volume of the cone = 1/3 × πr²h = 1/3 × π(25)² × 20 = 13083.33 m³
Question 7. How do you find the volume of a cone? Type below: ____________
Answer: V cone = 1/3 V cylinder V cone = 1/3 πr²h
13.2 Independent Practice – Volume of Cones – Page No. 409
Find the volume of each cone. Round your answers to the nearest tenth if necessary. Use 3.14 for π.
![lesson 1 problem solving practice volume of cylinders answer key Go Math Grade 8 Answer Key Chapter 13 Volume Lesson 2: Volume of Cones img 11](https://i0.wp.com/gomathanswerkey.com/wp-content/uploads/2020/08/Go-Math-Grade-8-Answer-Key-Chapter-13-Volume-img-11.jpg?resize=229%2C138&ssl=1)
Answer: 410.3 mm³
Explanation: Radius r = 7 mm height = 8 mm Volume of cone = 1/3 πr²h Volume = 1/3(3.14)(7)²(8) Volume = 410.29 mm³ Volume = 410.3 mm³
![lesson 1 problem solving practice volume of cylinders answer key Go Math Grade 8 Answer Key Chapter 13 Volume Lesson 2: Volume of Cones img 12](https://i0.wp.com/gomathanswerkey.com/wp-content/uploads/2020/08/Go-Math-Grade-8-Answer-Key-Chapter-13-Volume-img-12.jpg?resize=171%2C221&ssl=1)
Answer: 25.1 in 3
Explanation: Radius r = 2 in Height = 6 in Volume of cone = 1/3 πr²h Volume = 1/3(3.14)(2)²(6) Volume = 25.12 in 3 Volume = 25.1 in 3
Lesson 2 Extra Practice Volume of Cones Answers Key Question 10. A cone has a diameter of 6 centimeters and a height of 11.5 centimeters. _________ cm 3
Answer: 108.3 cm 3
Explanation: Diameter of base = 6 cm Radius = 6/2 cm = 3 cm Height = 11.5 cm Volume of cone = 1/3 πr²h Volume = 1/3(3.14)(3)² (11.5) Volume = 108.33 cm 3 Volume = 108.3 cm 3
Question 11. A cone has a radius of 3 meters and a height of 10 meters. _________ m 3
Answer: 94.2 m 3
Explanation: Radius r = 3 m Height = 10 m Volume of cone = 1/3 πr²h Volume = 1/3(3.14)(3)²(10) Volume = 94.2 m 3
Round your answers to the nearest tenth if necessary. Use 3.14 for π.
Question 12. Antonio is making mini waffle cones. Each waffle cone is 3 inches high and has a radius of \(\frac{3}{4}\) inch. What is the volume of a waffle cone? _________ in 3
Answer: 1.8 in 3
Explanation: Radius = 3/4 in Radius r = 0.75 in Height = 3 in Volume of each waffle cone = 1/3 πr²h Volume = 1/3 (3.14) (0.75)² (3) Volume = 1.76625 in 3 Volume = 1.8 in 3
Question 13. A snack bar sells popcorn in cone-shaped containers. One container has a diameter of 8 inches and a height of 10 inches. How many cubic inches of popcorn does the container hold? _________ in 3
Answer: 167.5 in 3
Explanation: Diameter of base = 8 in Radius = 8/2 in = 4 in Height = 10 in Volume of cone = 1/3 πr²h Volume = 1/3 (3.14) (4)² (10) Volume = 167.466 in 3 Volume = 167.5 in 3
Question 14. A volcanic cone has a diameter of 300 meters and a height of 150 meters. What is the volume of the cone? _________ m 3
Answer: 3534291.7 m 3
Explanation: Diameter of base = 300 m Radius = 300/2 m = 150 m Height = 150 m Volume of cone = 1/3 πr²h Volume = 1/3 (3.14) (150)² (150) Volume = 3534291.735 m 3 Volume = 3534291.7 m 3
The volume of Cones Answers Key Question 15. Multistep Orange traffic cones come in a variety of sizes. Approximate the volume, in cubic inches, of a traffic cone that has a height of 2 feet and a diameter of 10 inches. Use 3.14 for π. _________ in 3
Answer: 628 in³
Explanation: The radius of the cone is Diameter/2 = 10/2 = 5 The height of the cone is 2 ft = 2 . 12 = 24 in Vcone = 1/3 πr²h Vcone = 1/3 (3.14) (5)² (24) Vcone = 628 in³
Find the missing measure for each cone. Round your answers to the nearest tenth if necessary. Use 3.14 for π.
Question 16. radius = _______ height = 6 in. volume = 100.48 in3 _________ in.
Answer: radius = 4 in. 4 in.
Explanation: Let radius be R. Height = 6 in Volume = 100.4 in Volume of cone = 1/3 πr²h √(3v/hπ) = R √((3 × 100.48)/(18.84)) = R √(301.44/18.84) = R R = √(16) R = 4 in
Question 17. diameter = 6 cm height = _______ volume = 56.52 cm 3 _______ cm
Answer: height = 6 cm h = 6 cm
Explanation: Let height be h Diameter = 6 cm Radius = 6/2 = 3 cm Volume = 56.52 cm Volume of cone = 1/3 πr²h (3V/r²h) = h (3 × 56.52)/(3² × 3.14) = h 169.56/28.26 = h h = 6 cm
Question 18. The diameter of a cone-shaped container is 4 inches, and its height is 6 inches. How much greater is the volume of a cylinder-shaped container with the same diameter and height? Round your answer to the nearest hundredth. Use 3.14 for π. Type below: ____________
Answer: The volume of the cylinder is 50.24 in³ greater than the volume of the cone.
Explanation: The diameter of a cone, d = 4 inch radius of a cone, r = d/2 = 4/2 = 2 inches height of a cone, h = 6 inches. So, the volume of a cone, V cone = 1/3 πr²h = 1/3 (3.14) (2)² (6) = 25.12 in³ And the volume of a cylinder with the same diameter and height, V cylinder = πr²h = (3.14) (2)² (6) = 75.36 in³ The volume of the cylinder is 50.24 in³ greater than the volume of the cone.
FOCUS ON HIGHER ORDER THINKING – Volume of Cones – Page No. 410
Question 19. Alex wants to know the volume of sand in an hourglass. When all the sand is in the bottom, he stands a ruler up beside the hourglass and estimates the height of the cone of sand. a. What else does he need to measure to find the volume of sand? ____________
Answer: To find the volume of the sand, he needs to measure the radius of the base of the hourglass.
Question 19. b. Make a Conjecture If the volume of sand is increasing at a constant rate, is the height increasing at a constant rate? Explain. ____________
Answer: The volume of the cone is linearly proportional to the height of the cone. Therefore, if the volume is increasing at a constant rate, the height is also increasing at a constant rate.
Question 20. Problem Solving The diameter of a cone is x cm, the height is 18 cm, and the volume is 301.44 cm 3 . What is x? Use 3.14 for π. ________ cm
Answer: 8 cm
Explanation: V cone = 1/3 πr²h 301.44 = 1/3 . 3.14 . r² . 18 r² = 904.32/56.52 r² = 16 r = 4 cm The diameter of the circle is twice its radius, therefore x = 2 . r x = 2 . 4 x = 8 cm
Question 21. Analyze Relationships A cone has a radius of 1 foot and a height of 2 feet. How many cones of liquid would it take to fill a cylinder with a diameter of 2 feet and a height of 2 feet? Explain. ________ cones
Answer: 3 cones
Explanation: The diameter of the base of the cylinder is 2 feet, which means that its radius is 1 foot. Its height is 2 feet. The volume of this cylinder is V cylinder = πr²h V cylinder = (3.14) (1)² (2) V cylinder = 6.28 The radius of the cone is 1 foot and the height of the cone is 2 feet. The volume of the cone is: V cone = 1/3 πr²h V cone = 1/3 (3.14) (1)² (2) V cone = 1/3 × 6.28 V cone = 1/3 . V cylinder V cone = 2.09 It would take 3 cones of liquid to fill the cylinder.
Question 22. Critique Reasoning Herb knows that the volume of a cone is one third that of a cylinder with the same base and height. He reasons that a cone with the same height as a given cylinder but 3 times the radius should therefore have the same volume as the cylinder, since \(\frac{1}{3}\) ⋅ 3 = 1. Is Herb correct? Explain. ____________
Answer: The volume of the given cylinder is V cylinder = πr²h The volume of the cone with the same height h as a given cylinder but 3 times the radius r is V cone = 1/3 π(3r)²h V cone = 3 πr²h V cone = 3 V cylinder As we can see, Herb is not correct. The volume of the cone is not equal to the volume of the cylinder. But it is three times the volume of the cylinder.
Guided Practice – Volume of Spheres – Page No. 414
Question 1. Vocabulary A sphere is a three-dimensional figure with all points _____ from the center. Type below: ____________
Answer: A sphere is a three-dimensional figure with all points at equal distances from the center.
Lesson 13.2 Volume of Cones Practice and Problem Solving a/b Answers Question 2. Vocabulary The _____ is the distance from the center of a sphere to a point on the sphere. Type below: ____________
Answer: radius
Explanation: The radius is the distance from the center f the sphere to a point on the sphere
Find the volume of each sphere. Round your answers to the nearest tenth if necessary. Use 3.14 for π.
![lesson 1 problem solving practice volume of cylinders answer key Go Math Grade 8 Answer Key Chapter 13 Volume Lesson 3: Volume of Spheres img 13](https://i0.wp.com/gomathanswerkey.com/wp-content/uploads/2020/08/Go-Math-Grade-8-Answer-Key-Chapter-13-Volume-img-13.jpg?resize=156%2C118&ssl=1)
Answer: 4.12 in 3
Explanation: V = 4/3πr³ V = 4/3 (3.14) (1)³ V = 4.12 in 3
![lesson 1 problem solving practice volume of cylinders answer key Go Math Grade 8 Answer Key Chapter 13 Volume Lesson 3: Volume of Spheres img 14](https://i0.wp.com/gomathanswerkey.com/wp-content/uploads/2020/08/Go-Math-Grade-8-Answer-Key-Chapter-13-Volume-img-14.jpg?resize=185%2C124&ssl=1)
Answer: 4186.7 cm³
Explanation: Diameter = 20 cm Radius r = 20/2 = 10 cm Volume of sphere = 4/3πr³ Volume = 4/3 (3.14) (10)³ Volume = 4186.66 cm³ Volume = 4186.7 cm³
Question 5. A sphere has a radius of 1.5 feet. _______ ft 3
Answer: 14.1 ft³
Explanation: Radius r = 1.5 ft The volume of the sphere = 4/3πr³ Volume = 4/3 (3.14) (1.5)³ Volume = 14.13 ft³ Volume = 14.1 ft³
Question 6. A sphere has a diameter of 2 yards. _______ yd 3
Answer: 4.2 yd³
Explanation: Diameter = 2 yards Radius r = 2/2 yards Radius r = 1 yd Volume of sphere = 4/3πr³ Volume = 4/3 (3.14) (1)³ Volume = 4.1866 yd³ Volume = 4.2 yd³
Question 7. A baseball has a diameter of 2.9 inches. Find the volume of the baseball. Round your answer to the nearest tenth if necessary. Use 3.14 for π. _______ in 3
Answer: 12.8 in³
Explanation: Diameter of baseball = 2.9 in Radius r = 2.9/2 in Radius of baseball = 1.45 in The volume of the sphere = 4/3πr³ Volume = 4/3 (3.14) (1.45)³ Volume = 12.763 in³ Volume = 12.8 in³
Lesson 13.3 Volume of Spheres Practice and Problem Solving a/b Question 8. A basketball has a radius of 4.7 inches. What is its volume to the nearest cubic inch? Use 3.14 for π. _______ in 3
Answer: 1304 in³
Explanation: Radius of baseball = 4.7 in The volume of the sphere = 4/3πr³ Volume = 4/3 (3.14) (4.7)³ Volume = 1304.0168 in³ Volume = 1304 in³
![lesson 1 problem solving practice volume of cylinders answer key Go Math Grade 8 Answer Key Chapter 13 Volume Go Math Grade 8 Answer Key Chapter 13 Volume img 15 img 15](https://i0.wp.com/gomathanswerkey.com/wp-content/uploads/2020/08/Go-Math-Grade-8-Answer-Key-Chapter-13-Volume-img-15.jpg?resize=301%2C152&ssl=1)
Answer: The volume of the cylinder is V cylinder = πr²h Since the ball touches the bottom, top, and sides, then the height of the cylinder will be equal to 2r. V cylinder = πr²(2r) = 2πr³ On the other hand, the volume of the sphere is V sphere = 4/3 πr³ The volume of the empty space inside the cylindrical box is found by subtracting the volume of the sphere from the volume of the cylinder V cylinder – V sphere = 2πr³ – 4/3 πr³ = (2 – 4/3)πr³ = 2/3πr³
Question 9. b. Find an expression for the volume of the cubic box. Type below: _______________
Answer: The volume of a cube with side a is V cube = a³ Since the ball touches the bottom, top, and sides, then the side of the cube will be equal to 2r. V cube = (2r)³ V cube = 8r³
Question 9. c. About what portion of the space inside the cubic box is empty? Explain Type below: _______________
Answer: The volume of the empty space inside the cubical box is found by subtracting the volume of the sphere from the volume of the cube: V cube – V sphere = 8r³ – 4/3 πr³ = (8 – 4/3π)r³ = (8 – 4.2)r³ = 3.8r³
Question 10. Explain the steps you use to find the volume of a sphere. Type below: _______________
Answer: Step 1: The radius of the sphere is found out. Step 2: The volume of the sphere is 4/3 πr³; where R is the radius. Step 3: Put the value of radius in the equation of volume. Step 4: Calculate the volume.
13.3 Independent Practice – Volume of Spheres – Page No. 415
Question 11. radius of 3.1 meters _______ m 3
Answer: 124.7 m³
Explanation: The volume of the sphere with a radius of 3.1 meter is 4/3 πr³ V = 4/3 . (3.14) . (3.1)³ V = 124.7 m³
Question 12. diameter of 18 inches _______ in 3
Answer: 3052.1 in³
Explanation: The diameter of the sphere is 18 inches, which means that its radius is 9 inches. The volume of the sphere is V = 4/3 πr³ V = 4/3 . (3.14) . (9)³ V = 3052.08 in³ V = 3052.1 in³
Volume of Cylinders Cones and Spheres Iready Answers Question 13. r = 6 in. _______ in 3
Answer: 904.3 in³
Explanation: The volume of the sphere with a radius of 6 inches is V = 4/3 πr³ V = 4/3 (3.14) (6)³ V = 904.32 V = 904.3 in³
Question 14. d = 36 m _______ m 3
Answer: 24416.6 m³
Explanation: d = 36 m radius r = 36/2 = 18 m Volume = 4/3 πr³ = 4/3 (3.14) (18)³ = 24416.64 Volume = 24416.6 m³
![lesson 1 problem solving practice volume of cylinders answer key Go Math Grade 8 Answer Key Chapter 13 Volume Lesson 3: Volume of Spheres img 16](https://i0.wp.com/gomathanswerkey.com/wp-content/uploads/2020/08/Go-Math-Grade-8-Answer-Key-Chapter-13-Volume-img-16.jpg?resize=170%2C125&ssl=1)
Answer: 5572.5 cm³
Explanation: The volume of the sphere with a radius of 11 centimeters is V = 4/3 πr³ V = 4/3 (3.14) (11)³ V = 5572.5 cm³
![lesson 1 problem solving practice volume of cylinders answer key Go Math Grade 8 Answer Key Chapter 13 Volume Lesson 3: Volume of Spheres img 17](https://i0.wp.com/gomathanswerkey.com/wp-content/uploads/2020/08/Go-Math-Grade-8-Answer-Key-Chapter-13-Volume-img-17.jpg?resize=164%2C125&ssl=1)
Answer: 8.2 feet³
Explanation: The diameter of the sphere is 2.5 feet, which means that its radius is 1.25 feet. The volume of the sphere is V = 4/3 πr³ V = 4/3 . (3.14) . (1.25)³ V = 8.2 feet³
The eggs of birds and other animals come in many different shapes and sizes. Eggs often have a shape that is nearly spherical. When this is true, you can use the formula for a sphere to find their volume.
Question 17. The green turtle lays eggs that are approximately spherical with an average diameter of 4.5 centimeters. Each turtle lays an average of 113 eggs at one time. Find the total volume of these eggs, to the nearest cubic centimeter. _______ cm 3
Answer: 5389 cm³
Explanation: The diameter of an egg (sphere) is 4.5 centimeters, which means that its radius is 2.25 centimeters. The volume of a single egg is V = 4/3 πr³ V = 4/3 (3.14) (2.25)³ V = 47.68875 cm³ Therefore, the total volume of 113 eggs is 113 . V = 113(47.68875) = 5388.82875 = 5389 cm³
Question 18. Hummingbirds lay eggs that are nearly spherical and about 1 centimeter in diameter. Find the volume of an egg. Round your answer to the nearest tenth. _______ cm 3
Answer: 0.5 cm³
Explanation: The diameter of an egg (sphere) is 1 centimeter, which means that its radius is 0.5 centimeters. The volume of a single egg is V = 4/3 πr³ V = 4/3 (3.14) (0.5)³ V = 0.5 cm³
Question 19. Fossilized spherical eggs of dinosaurs called titanosaurid sauropods were found in Patagonia. These eggs were 15 centimeters in diameter. Find the volume of an egg. Round your answer to the nearest tenth. _______ cm 3
Answer: 1766.25 cm³
Explanation: Diameter of an egg = 15 cm Its radius = 15/2 = 7.5 cm Volume = 4/3 πr³ V = 4/3 (3.14) (7.5)³ V = 1766.25 cm³
Volume and Surface Area of Spheres Question 20. Persevere in Problem Solving An ostrich egg has about the same volume as a sphere with a diameter of 5 inches. If the eggshell is about \(\frac{1}{12}\) inch thick, find the volume of just the shell, not including the interior of the egg. Round your answer to the nearest tenth. _______ in 3
Answer: 6.8 in³
Explanation: Diameter including the eggshell = 5 + (2 . 1/2) = (5 + 1/6) in = 5.166 in Radius including eggshell = 5.166/2 = 2.5833 in Volume = 4/3 πr³ Volume = 4/3 (3.14) (2.5833)³ =72.176 in³ Volume with shell = 72.2 in³ Radius excluding shell = 5/2 = 2.5 in Volume = 4/3 (3.14) (2.5)³ = 65.416 in³ Volume (without shell) = 65.4 in³ Volume of shell = Total volume – Inner Volume = 72.2 – 65.4 = 6.8 in³
![lesson 1 problem solving practice volume of cylinders answer key Go Math Grade 8 Answer Key Chapter 13 Volume Lesson 3: Volume of Spheres img 18](https://i0.wp.com/gomathanswerkey.com/wp-content/uploads/2020/08/Go-Math-Grade-8-Answer-Key-Chapter-13-Volume-img-18.jpg?resize=111%2C118&ssl=1)
Answer: 5/3πr³
Explanation: The radius of the hemisphere = r The radius of cylinder = r Height of cylinder = r Step 1: Find the formula for the volume of a hemisphere The volume of hemisphere = 4/3 π/2 r³ = 2/3πr³ Step 2: Find the formula for the volume of a cylinder The volume of the cylinder = πr²h =πr³ Step 3: Add both the volume expressions: Total volume = 2/3πr³ + πr³ = 5/3πr³
Volume of Spheres – Page No. 416
Question 22. Critical Thinking Explain what happens to the volume of a sphere if you double the radius. Type below: _____________
Answer: Let Radius = r Volume V1 = 4/3πr³ Radius = 2r Volume V2 = 4/3π(2r)³ = 8 . 4/3πr³ = 8 V1 = 8(initial volume) By doubling the radius of the sphere we make the volume 8 times the initial value.
![lesson 1 problem solving practice volume of cylinders answer key Go Math Grade 8 Answer Key Chapter 13 Volume Lesson 3: Volume of Spheres img 19](https://i0.wp.com/gomathanswerkey.com/wp-content/uploads/2020/08/Go-Math-Grade-8-Answer-Key-Chapter-13-Volume-img-19.jpg?resize=171%2C244&ssl=1)
Answer: 12.3 in³
Explanation: Radius of the ball = 1.25 inch Height of the cylinder = (2 × 1.25) × 3 = (2.5) × 3 = 7.5 in radius of base of cylinder = 1.25 in. Volume of cylinder = πr²h = (3.14) (1.25)² (7.5) = 36.7968 = 36.8 in³ Volume of a ball (all three) = 3 × 4/3πr³ = 4 (3.14) (1.25)³ = 24.53125 in³ = 24.5 in³ Volume of empty space = Volume of cylinder – Volume of ball = 36.8 – 24.5 = 12.3 in³
Question 24. Critique Reasoning A sphere has a radius of 4 inches, and a cube-shaped box has an edge length of 7.5 inches. J.D. says the box has a greater volume, so the sphere will fit in the box. Is he correct? Explain. _____________
Answer: The volume of sphere = 4/3πr³ = 4/3 (3.14) (4)³ = 267.9466 = 268 The volume of cube = (7.5)³ = 421.875 =421.9 The volume of cube > Volume of a sphere But the base of the cube has an area of (7.5 × 7.5) = 56.25 while the cross-action area of the sphere. πr² = (3.14) (4)² = 50.24 The cross-section area of the cube is less than that of a sphere. thus J.D. is wrong and the ball (sphere) will not fit in the cube.
Question 25. Critical Thinking Which would hold the most water: a bowl in the shape of 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. _____________
Answer: The volume of a sphere with radius r is V sphere = 4/3πr³ Therefore, the volume of a hemisphere is V hemisphere = V sphere/2 V hemisphere = 2/3πr³ The volume of a cylinder with radius r and height r is V cylinder = πr²h V cylinder = πr³ The volume of a cone with radius r and height r is V cone = 1/3πr²h V cone = 1/3πr³ V cone < V hemisphere < V cylinder Therefore, the cylindrical glass with radius r and height r will hold the most water.
8th Grade Review for Volume of Cylinders, Cones, and Spheres Answer Key Question 26. Analyze Relationships Hari has models of a sphere, a cylinder, and a cone. The sphere’s diameter and the cylinder’s height are the same, 2r. The cylinder has radius r. The cone has diameter 2r and height 2r. Compare the volumes of the cone and the sphere to the volume of the cylinder. Type below: _____________
Answer: Radius of sphere = 2r/2 = r Volume of sphere = 4/3πr³ The radius of cylinder = r Height of cylinder = 2r volume of cylinder = πr²(2r) V cylinder = 2πr³ Radius of cone = 2r/2 = r Height of cone = 2r Volume of cone = 1/3 πr²(2r) V cone = 2/3πr³ Volume of cylinder > Volume of sphere > Volume of cone 2πr³ > 4/3πr³ > 2/3πr³
Question 27. A spherical helium balloon that is 8 feet in diameter can lift about 17 pounds. What does the diameter of a balloon need to be to lift a person who weighs 136 pounds? Explain. _______ feet
Answer: Diameter of ballon = 8 ft Weight it could lift = 17 pound Volume = 4/3 π(8/2)³ = 4³(4π/3) 4³/x(4π/3) = 17/36 1/x = 1/8 × 3/4π × 1/48 x = 4π/3 . 4³ . 2³ x = 4/3. π . 8³ The volume of ballon which can lift 136 pounds is equal to 4/3. π . 8³ The radius of that ballon = 8ft Diameter = 8 . 2 = 16 ft
Ready to Go On ? – Model Quiz – Page No. 417
13.1 Volume of Cylinders
Find the volume of each cylinder. Round your answers to the nearest tenth if necessary. Use 3.14 for π.
![lesson 1 problem solving practice volume of cylinders answer key Go Math Grade 8 Answer Key Chapter 13 Volume Lesson 3: Model Quiz img 20](https://i0.wp.com/gomathanswerkey.com/wp-content/uploads/2020/08/Go-Math-Grade-8-Answer-Key-Chapter-13-Volume-img-20.jpg?resize=133%2C128&ssl=1)
Answer: 904.8 ft³
Explanation: Radius of base = 6 ft Height of cylinder = 8 ft The volume of cylinder = πr²h Volume = (3.14) (6)² (8) Volume = 904.77 ft³ Volume = 904.8 ft³
Volume of Cylinders, Cones, and Spheres Iready Answers Question 2. A can of juice has a radius of 4 inches and a height of 7 inches. What is the volume of the can? _______ in 3
Answer: 351.7 in³
Explanation: Radius if cylindrical can = 4 in Height of cylindrical can = 7 in The volume of cylinder = πr²h Volume = (3.14) (4)² (7) Volume = 351.68 in³ Volume = 351.7 in³
13.2 Volume of Cones
![lesson 1 problem solving practice volume of cylinders answer key Go Math Grade 8 Answer Key Chapter 13 Volume Lesson 3: Model Quiz img 21](https://i0.wp.com/gomathanswerkey.com/wp-content/uploads/2020/08/Go-Math-Grade-8-Answer-Key-Chapter-13-Volume-img-21.jpg?resize=134%2C173&ssl=1)
Answer: 565.2 cm³
Explanation: Radius of base of cone = 6 cm Height of cone = 15 cm Volume of cone = 1/3πr²h Volume = 1/3 (3.14) (4)² (7) Volume = 565.2 cm³
![lesson 1 problem solving practice volume of cylinders answer key Go Math Grade 8 Answer Key Chapter 13 Volume Lesson 3: Model Quiz img 22](https://i0.wp.com/gomathanswerkey.com/wp-content/uploads/2020/08/Go-Math-Grade-8-Answer-Key-Chapter-13-Volume-img-22.jpg?resize=169%2C185&ssl=1)
Answer: 3014.4 in³
Explanation: The radius of the base of cone = 12 in Height of cone = 20 in The volume of cone = 1/3πr²h Volume = 1/3 (3.14) (12)² (20) Volume = 3014.4 in³
13.3 Volume of Spheres
![lesson 1 problem solving practice volume of cylinders answer key Go Math Grade 8 Answer Key Chapter 13 Volume Lesson 3: Model Quiz img 23](https://i0.wp.com/gomathanswerkey.com/wp-content/uploads/2020/08/Go-Math-Grade-8-Answer-Key-Chapter-13-Volume-img-23.jpg?resize=154%2C117&ssl=1)
Answer: 113 in³
Explanation: Radius of sphere = 3 ft Volume of sphere = 4/3πr³ Volume = 4/3 (3.14) (3)³ Volume = 113.04 ft³ Volume = 113 in³
![lesson 1 problem solving practice volume of cylinders answer key Go Math Grade 8 Answer Key Chapter 13 Volume Lesson 3: Model Quiz img 24](https://i0.wp.com/gomathanswerkey.com/wp-content/uploads/2020/08/Go-Math-Grade-8-Answer-Key-Chapter-13-Volume-img-24.jpg?resize=170%2C137&ssl=1)
Answer: 1149.8 cm³
Explanation: Diameter = 13 cm Radius = 13/2 cm = 6.5 cm Volume of sphere = 4/3πr³ Volume = 4/3 (3.14) (6.5)³ Volume = 1149.7633 cm³ Volume = 1149.8 cm³
ESSENTIAL QUESTION
Question 7. What measurements do you need to know to find the volume of a cylinder? a cone? a sphere? Type below: ___________
Answer: Sphere: To find the volume of the sphere, the radius is to be measured. Cylinder: To measure the volume of the cylinder, we need to find out the base radius of the base of the cylinder along with the height of the cylinder. Cone: To calculate the volume of the cone, we need to calculate the base radius of the base of the cone along with the height of the cone.
Explanation: The volume of sphere = 4/3 πr³ Sphere: For finding the volume of the sphere, the radius is to be measured The volume of Cylinder = πr²h Cylinder: To calculate the volume of the cylinder, we need to find out the base radius of the base of the cylinder along with the height of the cylinder The volume of Cone = 1/3 πr²h Cone: To calculate the volume of the cone, we need to measure the base radius of the base of the cone along with the height of the cone
Selected Response – Mixed Review – Page No. 418
Question 1. The bed of a pickup truck measures 4 feet by 8 feet. To the nearest inch, what is the length of the longest thin metal bar that will lie flat in the bed? Options: a. 11 ft 3 in. b. 10 ft 0 in. c. 8 ft 11 in. d. 8 ft 9 in.
Answer: d. 8 ft 9 in.
Explanation: The length of the longest thin metal bar that will lie flat in the bed’s equal to the length of the bed’s hypotenuse. Let a = 4 and b = 8. Using the Pythagorean Theorem a² + b² = c² 4² + 8² = c² 16 + 64 = c² 80 = c² Rounding the length of the hypotenuse to the nearest tenth of a foot c = 8.9 ft Therefore, the length of the longest thin metal bar that will lie flat in the bed is 8 ft. 9 in.
![lesson 1 problem solving practice volume of cylinders answer key Go Math Grade 8 Answer Key Chapter 13 Volume Lesson 3: Mixed Review img 25](https://i0.wp.com/gomathanswerkey.com/wp-content/uploads/2020/08/Go-Math-Grade-8-Answer-Key-Chapter-13-Volume-img-25.jpg?resize=140%2C117&ssl=1)
Answer: c. 1,091.6 cubic yards
Explanation: Diameter of the base of the cylinder = 11.4 yd Radius = 11.4/2 yd = 5.7 yd Height = 10.7 ys Volume of cylinder = πr²h Volume = (3.14) (5.7)² (10.7) Volume = 1091.599 yd³ Volume = 1091.6 yd³
Question 3. Rhett made mini waffle cones for a birthday party. Each waffle cone was 3.5 inches high and had a radius of 0.8 inches. What is the volume of each cone to the nearest hundredth? Options: a. 1.70 cubic inches b. 2.24 cubic inches c. 2.34 cubic inches d. 8.79 cubic inches
Answer: c. 2.34 cubic inches
Explanation: Height of each waffle cone = 3.5 in Radius of base = 0.8 in Volume of cone = 1/3 πr²h Volume = 1/3 (3.14) (0.8)² (3.5) Volume = 2.344533 in³ Volume = 2.34 in³
Question 4. What is the volume of a cone that has a height of 17 meters and a base with a radius of 6 meters? Use 3.14 for π and round to the nearest tenth. Options: a. 204 cubic meters b. 640.6 cubic meters c. 2,562.2 cubic meters d. 10,249 cubic meters
Answer: b. 640.6 cubic meters
Explanation: Height of the cone = 17 m Radius of base = 6 m Volume of cone = 1/3 πr²h Volume = 1/3 (3.14) (6)² (17) Volume = 640.56 m³ Volume = 640.6 m³
![lesson 1 problem solving practice volume of cylinders answer key Go Math Grade 8 Answer Key Chapter 13 Volume Lesson 3: Mixed Review img 26](https://i0.wp.com/gomathanswerkey.com/wp-content/uploads/2020/08/Go-Math-Grade-8-Answer-Key-Chapter-13-Volume-img-26.jpg?resize=176%2C123&ssl=1)
Answer: b. 5,572.5 cubic centimeters
Explanation: Diameter of the base of the sphere = 22 cm Radius = 22/2 yd = 11 cm Volume of sphere = 4/3 πr³ Volume = 4/3 (3.14) (11)³ Volume = 5572.4533 cm³ Volume = 5572.5 cm³
![lesson 1 problem solving practice volume of cylinders answer key Go Math Grade 8 Answer Key Chapter 13 Volume Lesson 3: Mixed Review img 27](https://i0.wp.com/gomathanswerkey.com/wp-content/uploads/2020/08/Go-Math-Grade-8-Answer-Key-Chapter-13-Volume-img-27.jpg?resize=133%2C145&ssl=1)
Answer: 8.574 cm³
Explanation: The radius of the cylinder as well as the hemisphere = 1.6 cm Height = 6.2 cm the volume of the hemisphere = 2/3 πr³ the volume of the hemisphere = 2/3 (3.14) (1.6)³ the volume of the hemisphere = 8.574 cm³
Question 6. b. What is the volume of the cylinder? _______ cm 3
Answer: 49.838 cm³
Explanation: The volume of cylinder = πr²h = (3.14) (1.6)² (6.2) = 49.838 cm³
Question 6. c. What is the volume of the whole figure? _______ cm 3
Answer: 58.4 cm³
Explanation: Total volume = Volume of cylinder + volume of a hemisphere Total volume = 8.574 cm³ + 49.838 cm³ Total volume = 58.4 cm³
Conclusion:
Download Go Math Grade 8 Answer Key Chapter 13 Volume for free of cost. Self-study is also possible with the help of HMH Go Math Grade 8 Solution Key. Begin your practice now by referring to Go Math Grade 8 Chapter 13 Volume Solution Key. Every student love to practice maths with the help of the Go Math Grade 8 Solution Key. Each and every problem is explained in a detailed way to help the students to practice in the best way.
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Volume of Cylinders
A cylinder is a solid with two congruent circles joined by a curved surface.
![volume of cylinder volume of cylinder](https://www.onlinemathlearning.com/image-files/volume-cylinder.png)
In the above figure, the radius of the circular base is r and the height is h.
The volume of the cylinder is the area of the base × height. Since the base is a circle and the area of a circle is πr 2 then the volume of the cylinder is πr 2 × h.
Volume of cylinder = πr 2 h
Surface Area of cylinder = 2πr 2 + 2πrh
Calculate the volume of a cylinder where:
a) the area of the base is 30 cm 2 and the height is 6 cm. b) the radius of the base is 14 cm and the height is 10 cm.
Sometimes you may be required to calculate the volume of a hollow cylinder or tube or pipe.
Volume of hollow cylinder: = πR 2 h – πr 2 h = πh (R 2 – r 2 )
The figure shows a section of a metal pipe. Given the internal radius of the pipe is 2 cm, the external radius is 2.4 cm and the length of the pipe is 10 cm. Find the volume of the metal used.
Solution: The cross section of the pipe is a ring: Area of ring = [ π (2.4) 2 – π (2) 2 ]= 1.76 π cm 2
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A barrel of crude oil contains about 5.61 cubic feet of oil. How many barrels of oil are contained in 1 mile (5280 feet) of a pipeline that has an inside 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? | barrels | |||
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A pan for baking French bread is shaped like half a cylinder. It is 12 inches long and 3.5 inches in diameter. What is the volume of uncooked dough that would fill this pan?
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Explain the Error A student said the volume of a cylinder with a 3-inch diameter is two times the volume of a cylinder with the same height and a 1.5-inch radius. What is the error?
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Communicate Mathematical Ideas Explain how you can find the height of a cylinder if you know the diameter and the volume. Include an example with your explanation.
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.
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Volume of a Cylinder
The worksheets below can be used to help teach students how to calculate the volumes of cylinders. The basic level worksheets do not include decimal measurements. The advanced level includes decimals and/or fractional measurements.
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From this page you can download a collection of worksheets on calculating the volumes of rectangular prisms.
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Volume of cylinder practice
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Volume of Cylinders Notes & Practice | + Interactive Notebook Pages
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Volume of Cylinders Missing Dimensions Notes & Practice (Distance Learning)
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Volume of Cylinders Word Problem Practice PLUS Critical Writing
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Volume of a Cylinder Practice Problems/Engaging Questions
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Volume of Cylinders Task Cards | Math Center Practice Activity
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Volume of Cylinders , Cones, & Spheres NOTES & Practice
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Volume of Cylinders Notes & Practice | Guided Notes | + Interactive Notebook
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Volume of Prisms, Cylinders , Pyramids, Cones, and Spheres notes & practice
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Volume of Composite Figures with Cylinders , Cones & Spheres | Printable Practice
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Volume of a Cylinder , Cone, and Sphere - 3 Practice Worksheets 8.G.C.9
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Volume of Cylinders & Prisms: Notes & Practice
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Volume of Cylinders , Cones, & Spheres Practice Worksheet 8.7A
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Surface Area and Volume of Cylinders Guided Notes & Practice Worksheets
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Volume of Cylinders , Cones, & Spheres Sketch Notes & Practice
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Volume of a Cone, Cylinder , and Sphere - Free Practice or Quiz - 8.G.C.9
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Volume of Spheres, Cones and Cylinders Mixed Practice Digital Activity
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Circumference, Area, and Volume of Circles & Cylinders Practice
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Surface Area and Volume of Prisms, Cylinders , and Spheres Notes and Practice
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Volume of a Cylinder Practice Activities - Print & Digital
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Volume of Cylinders Guided Notes & Practice
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Volume of Cylinders , Cones, and Spheres Bundle (Notes & Practice )
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Volume of Regular Prisms and Cylinders Google Forms Quiz Practice
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Volume of Cylinders Digital Practice Activity
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Math Modeling Volume of Sphere, Cylinder , Pyramid, Cone, Practice Word Problems
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Lesson 1 Homework Practice Volume Of Cylinders
Lesson 1 Homework Practice Volume Of Cylinders - Displaying top 8 worksheets found for this concept.
Some of the worksheets for this concept are Answers lessons 12 1 and 12 2 name date period 8, Lesson 47 prisms and cylinders, Volumes of cylinders, , Practice a 10 6 volume of prisms and cylinders, Surface area prisms cylinders l1es1, By the mcgraw hill companies all rights, Lesson 47 prisms and cylinders.
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1. Answers (Lessons 12-1 and 12-2) NAME DATE PERIOD 8 in.
2. lesson 47: prisms and cylinders, 3. 7.2 volumes of cylinders, 5. practice a 10-6 volume of prisms and cylinders, 6. surface area: prisms & cylinders l1es1, 7. copyright by the mcgraw-hill companies, inc. all rights ..., 8. lesson 47: prisms and cylinders.
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COMMENTS
Volume of each cube = 1 in³ Volume of cylinder = 427in³. Lesson 13.1 Volume of Cylinders Practice and Problem Solving a/b Question 3. Find the volume of the cylinder to the nearest tenth. Use 3.14 for π. The volume of the cylinder is approximately _____ m 3. _____ m 3. Answer: The volume of the cylinder is approximately 1695.6 m 3. 1695.6m³ ...
Lesson 1 Problem-Solving Practice Volume of Cylinders 1. WATER STORAGE A cylindrical water tank has a diameter of 5.3 meters and a height of 9 meters. What is the maximum volume that the water tank can hold? Round to the nearest tenth. 2. PACKAGING A can of corn has a diameter of 6.6 centimeters and a height of 9.9 centimeters. How much
and freely. Find the volume of his model, which has a height of30. nch. s and a diam. _ LESSONVolume of Cones13. 2Practice and Problem Solving: DFind the volume of. each cone. Round. your answer to the nearest tenth if necessary. Use 3.14 for π. Show y. ur work by filling in the blan. s.
Find the volume of each figure. Round your answers to the nearest tenth if necessary. Use 3.14 for π π. A cylinder has a radius of 4 centimeters and a height of 40 centimeters. A cylinder has a radius of 8 meters and a height of 4 meters. Round your answer to the nearest tenth, if necessary. Use 3.14 forπ π.
Two fuel tanks with the dimensions shown have the same volume. What is the value of h? NAME _____ DATE _____ PERIOD _____ Course 3 • Chapter 7 Connect Algebra to Geometry Lesson 1 Problem-Solving Practice Volume of Cylinders 1. A cylindrical water tank has a diameter of 5.3 meters and a height of 9 meters. What is the maximum volume
1. Find the volume of cylinder with radius of 5.5 feet and a height of 11.4 feet. 2. Find the volume of cylinder with diameter of 12 inches and a height of 29 inches. ... Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the ...
A museum in Takayama City has three odaikos of similar size carved from a single tree trunk. The largest measures about 2.7 meters in both diameter and length, and weighs about 4.5 metric tons. Using the volume formula for a cylinder, approximate the volume of the drum to the nearest tenth. The radius of the drum is about _____ m.
Volume of Cylinders Practice and Problem Solving: C Solve. Use 3.14 for π. Round your answer to the nearest tenth, if necessary. Show your work. 1. A feeding trough was made by hollowing out half of a log. The trough is shaped like half a cylinder. It is 5 feet long and has an interior diameter of 1.5 feet.
Lesson 1 Homework Practice Volume of Cylinders Find the volume of each cylinder. Round to the nearest tenth. 1. ... ESTIMATION Match each cylinder with its approximate volume. 8.diameter = 4 cm, height = 3.6 cm a. 116 cm3 9.radius = 2.7 cm, height = 5 cm b. 115 cm3 10. radius = 3 cm, height = 4.1 cm c. 106 cm3
Grade 8 HMH Go Math - Answer Keys. Chapter 13:Volume; Lesson 1: Volume of Cylinders. Please share this page with your friends on FaceBook. Question 16 (request help) A barrel of crude oil contains about 5.61 cubic feet of oil. How many barrels of oil are contained in 1 mile (5280 feet) of a pipeline that has an inside diameter of 6 inches and ...
Volume of Cylinders Practice and Problem Solving: A/B Find the volume of each cylinder. Round your answer to the nearest tenth if necessary. Use 3.14 for π. 1. 2. _____ _____ 3. A cylindrical oil drum has a diameter of 2 feet and a height of 3 feet. What is the volume of the oil drum? _____ 4. New Oats cereal is packaged in a cardboard ...
Goal: Create a set of instructions for how to find the volume of a cylinder.
a cylinder. EXAMPLE 1 Finding the Volume of a Cylinder Find the volume of the cylinder. Round your answer to the nearest tenth. V = Bh Write formula for volume. = π (3)2(6) Substitute. = 54π ≈ 169.6 Use a calculator. The volume is about 169.6 cubic meters. EXAMPLE 2 Finding the Height of a Cylinder Find the height of the cylinder. Round ...
Lesson: 13.1 Volume of Cylinders Essential Question: ... Draw the cylinder with the dimensions show in the video and then show your work to solve for the volume. Pi is an _____ number because it does not _____. The 3 stands for _____, whereas the 2 is used only for _____. ...
Volume - Cylinder ES1Find the exact vo. ume =9)7 mVolume =10) The cross-section of a pipe has a width of 6 centimeter and he. ght of 15 centimeter. Calculate t. e volume of the pipe.Volume = Find the exact vo. )7 mVolume =63π m10) The cross-section of a pipe has a width of 6 centimeter and he. ght of 15 centimeter. Calculate t.
116 Course 3 • Chapter 8 Volume and Surface Area NAME _____ DATE _____ PERIOD _____ Copyright © The M cGraw-Hill Comp anies, Inc. Perm
This worksheet shows 9 cylinders. The height and radius of the bases are given. Students calculate the volume of each. Compare the volumes of two cylinders. Answer 14 questions that walk you through volume calculations step-by-step. Calculate the volumes of the cylinders in each of the word problems.
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Find step-by-step solutions and answers to Ready Mathematics Practice and Problem Solving Grade 8 - 9781495704857, as well as thousands of textbooks so you can move forward with confidence. ... Section Lesson 26: Understand Volume of Cylinders, Cones, and Spheres. Section Lesson 27: Performance task. ... Our resource for Ready Mathematics ...
7. 1.95 kg Practice and Problem Solving: C 1. 124.4 in3 2. 477.8 cm3 3. 120 m3 4. 20.2 cm3 5. 135 cm3 6. Marsha got the units confused. The volume of one marble is 7,234.5 mm3. Marsha needs to convert that volume to cm3, which is about 7.2 cm3. 7. Answers will vary. Sample answer: If you divide the volume of the container by the volume of 1 ...
Lisa Blagus Teach at the Beach. 5.0. (39) $1.75. PDF. This activity is a 5 page lesson on the volume of a cylinder, where students go the circus and find various cylinders to find the volume of. Problems include diameter and radius, and one of the questions has them come up with their own problem. Great activity to engage students.
Lesson 1 Homework Practice Volume of Rectangular Prisms Find the volume of each prism. 1. 7 yd 5 yd 9 yd 2. 10 mm 6 mm 3 mm 3. 9 in.1 4 in. 3 6 in.1 2 4. 12 ft 3 ft 6 ft 5. 4 m 4 m 13 m 6. 8 yd 2 yd1 2 5 yd3 4 7. MUSIC Find the volume of the CD box shown at the right. 8. TOYS Geneva's younger brother has a toy box that is 3.6 feet long, 2.4 ...
Lesson 1 Homework Practice Volume Of Cylinders - Displaying top 8 worksheets found for this concept.. Some of the worksheets for this concept are Answers lessons 12 1 and 12 2 name date period 8, Lesson 47 prisms and cylinders, Volumes of cylinders, , Practice a 10 6 volume of prisms and cylinders, Surface area prisms cylinders l1es1, By the mcgraw hill companies all rights, Lesson 47 prisms ...