\na.
\ni. Write an equation to determine the volume of the rectangular prism shown below.
\n
![\"Engage](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Engage-NY-Math-Grade-8-Module-5-Lesson-10-Exercise-Answer-Key-1.png\")
\nAnswer:
\nV = 8(6)(h)
\n= 48h
\nThe volume is 48h mm3<\/sup>.<\/p>\n
ii. Write an equation to determine the volume of the rectangular prism shown below. iii. Write an equation to determine the volume of the rectangular prism shown below. iv. Write an equation for volume, V, in terms of the area of the base, B. b. Using what you learned in part (a), write an equation to determine the volume of the cylinder shown below. Exercises 1\u20133<\/p>\n Exercise 1. b. What is the height? c. What is the volume of the rectangular prism? Exercise 2. b. What is the height? c. What is the volume of the right circular cylinder? Exercise 3. b. What is the height? c. What is the volume of the right circular cylinder? Exercises 4\u20136<\/p>\n Exercise 4. Exercise 5. Exercise 6. b. What do we know about the measure of \u2220OAB and \u2220OCD? c. What can you say about \u25b3OAB and \u25b3OCD? d. What is the ratio of the volume of water to the volume of the container itself? Question 1. Question 2. Question 3. Question 4. Question 5. Question 6. Question 1. Question 2. Engage NY Eureka Math 8th Grade Module 5 Lesson 10 Answer Key Eureka Math Grade 8 Module 5 Lesson 10 Exercise Answer Key Opening Exercise a. i. Write an equation to determine the volume of the rectangular prism shown below. Answer: V = 8(6)(h) = 48h The volume is 48h mm3. ii. Write an equation … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/80600"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=80600"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/80600\/revisions"}],"predecessor-version":[{"id":137611,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/80600\/revisions\/137611"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=80600"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=80600"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=80600"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n![\"Engage](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Engage-NY-Math-Grade-8-Module-5-Lesson-10-Exercise-Answer-Key-2.png\")
\nAnswer:
\nV = 10(8)(h)
\n= 80h
\nThe volume is 80h in3<\/sup>.<\/p>\n
\n![\"Engage](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Engage-NY-Math-Grade-8-Module-5-Lesson-10-Exercise-Answer-Key-3.png\")
\nAnswer:
\nV = 6(4)(h)
\n= 24h
\nThe volume is 24h cm3<\/sup>.<\/p>\n
\nV = Bh<\/p>\n
\n![\"Engage](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Engage-NY-Math-Grade-8-Module-5-Lesson-10-Exercise-Answer-Key-4.png\")
\nAnswer:
\nV = Bh
\n= 42<\/sup> \u03c0h
\n= 16\u03c0h
\nThe volume is 16\u03c0h cm3<\/sup>.<\/p>\n
\nUse the diagram to the right to answer the questions.
\n![\"Engage](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Engage-NY-Math-Grade-8-Module-5-Lesson-10-Exercise-Answer-Key-5.png\")
\na. What is the area of the base?
\nAnswer:
\nThe area of the base is (4.5)(8.2) in2<\/sup> or 36.9 in2<\/sup>.<\/p>\n
\nAnswer:
\nThe height of the rectangular prism is 11.7 in.<\/p>\n
\nAnswer:
\nThe volume of the rectangular prism is 431.73 in3<\/sup>.<\/p>\n
\nUse the diagram to the right to answer the questions.
\n![\"Engage](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Engage-NY-Math-Grade-8-Module-5-Lesson-10-Exercise-Answer-Key-6.png\")
\na. What is the area of the base?
\nAnswer:
\nA = \u03c022<\/sup>
\nA = 4\u03c0
\nThe area of the base is 4\u03c0 cm2<\/sup>.<\/p>\n
\nAnswer:
\nThe height of the right circular cylinder is 5.3 cm.<\/p>\n
\nAnswer:
\nV = (\u03c0r2<\/sup>)h
\nV = (4\u03c0)5.3
\nV = 21.2\u03c0
\nThe volume of the right circular cylinder is 21.2\u03c0 cm3<\/sup>.<\/p>\n
\nUse the diagram to the right to answer the questions.
\n![\"Engage](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Engage-NY-Math-Grade-8-Module-5-Lesson-10-Exercise-Answer-Key-7.png\")
\na. What is the area of the base?
\nAnswer:
\nA = \u03c062<\/sup>
\nA = 36\u03c0
\nThe area of the base is 36\u03c0 in2<\/sup>.<\/p>\n
\nAnswer:
\nThe height of the right circular cylinder is 25 in.<\/p>\n
\nAnswer:
\nV = (36\u03c0)25
\nV = 900\u03c0
\nThe volume of the right circular cylinder is 900\u03c0 in3<\/sup>.<\/p>\n
\nUse the diagram to find the volume of the right circular cone.
\n![\"Engage](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Engage-NY-Math-Grade-8-Module-5-Lesson-10-Exercise-Answer-Key-8.png\")
\nAnswer:
\nV = \\(\\frac{1}{3}\\) (\u03c0r2<\/sup>)h
\nV = \\(\\frac{1}{3}\\) (\u03c042<\/sup>)9
\nV = 48\u03c0
\nThe volume of the right circular cone is 48\u03c0 mm3<\/sup>.<\/p>\n
\nUse the diagram to find the volume of the right circular cone.
\n![\"Engage](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Engage-NY-Math-Grade-8-Module-5-Lesson-10-Exercise-Answer-Key-9.png\")
\nAnswer:
\nV = \\(\\frac{1}{3}\\) (\u03c0r2<\/sup>)h
\nV = \\(\\frac{1}{3}\\) (\u03c02.32<\/sup>)15
\nV = 26.45\u03c0
\nThe volume of the right circular cone is 26.45\u03c0 m3<\/sup>.<\/p>\n
\nChallenge: A container in the shape of a right circular cone has height h, and base of radius r, as shown. It is filled with water (in its upright position) to half the height. Assume that the surface of the water is parallel to the base of the inverted cone. Use the diagram to answer the following questions:
\n![\"Engage](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Engage-NY-Math-Grade-8-Module-5-Lesson-10-Exercise-Answer-Key-10.png\")
\na. What do we know about the lengths of AB and AO?
\nAnswer:
\nThen we know that |AB| = r, and |AO| = h.<\/p>\n
\nAnswer:
\n\u2220OAB and \u2220OCD are both right angles.<\/p>\n
\nAnswer:
\nWe have two similar triangles, \u25b3OAB and \u25b3OCD by AA criterion.<\/p>\n
\nAnswer:
\nSince \\(\\frac{|A B|}{|C D|}\\) = \\(\\frac{|A O|}{|C O|}\\), and |AO| = 2|OC|, we have \\(\\frac{|A B|}{|C D|}\\) = 2\\(\\frac{2|O C|}{|C O|}\\).
\nThen |AB| = 2|CD|.
\nUsing the volume formula to determine the volume of the container, we have V = \\(\\frac{1}{3}\\) \u03c0|AB|2<\/sup> |AO|.
\nBy substituting |AB| with 2|CD| and |AO| with 2|OC| we get:
\nV = \\(\\frac{1}{3}\\) \u03c0(2|CD|)2<\/sup> (2|OC|)
\nV = 8(\\(\\frac{1}{3}\\) \u03c0|CD|2<\/sup> |OC|), where \\(\\frac{1}{3}\\) \u03c0|CD|2<\/sup> |OC| gives the volume of the portion of the container that is filled with water.
\nTherefore, the volume of the water to the volume of the container is 1:8.<\/p>\nEureka Math Grade 8 Module 5 Lesson 10 Problem Set Answer Key<\/h3>\n
\nUse the diagram to help you find the volume of the right circular cylinder.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-8th-Grade-Module-5-Lesson-10-Problem-Set-Answer-Key-1.png\")
\nAnswer:
\nV = \u03c0r2<\/sup> h
\nV = \u03c0(1)2<\/sup> (1)
\nV = \u03c0
\nThe volume of the right circular cylinder is \u03c0 ft3<\/sup>.<\/p>\n
\nUse the diagram to help you find the volume of the right circular cone.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-8th-Grade-Module-5-Lesson-10-Problem-Set-Answer-Key-2.png\")
\nAnswer:
\nV = \\(\\frac{1}{3}\\) \u03c0r2<\/sup> h
\nV = \\(\\frac{1}{3}\\) \u03c0(2.8)2<\/sup> (4.3)
\nV = 11.237333\u2026\u03c0
\nThe volume of the right circular cone is about 11.2\u03c0 cm3<\/sup>.<\/p>\n
\nUse the diagram to help you find the volume of the right circular cylinder.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-8th-Grade-Module-5-Lesson-10-Problem-Set-Answer-Key-3.png\")
\nAnswer:
\nIf the diameter is 12 mm, then the radius is 6 mm.
\nV = \u03c0r2<\/sup> h
\nV = \u03c0(6)2<\/sup> (17)
\nV = 612\u03c0
\nThe volume of the right circular cylinder is 612\u03c0 mm3<\/sup>.<\/p>\n
\nUse the diagram to help you find the volume of the right circular cone.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-8th-Grade-Module-5-Lesson-10-Problem-Set-Answer-Key-4.png\")
\nAnswer:
\nIf the diameter is 14 in., then the radius is 7 in.
\nV = \\(\\frac{1}{3}\\) \u03c0r2<\/sup> h
\nV = \\(\\frac{1}{3}\\) \u03c0(7)2<\/sup> (18.2)
\nV = 297.26666\u2026\u03c0
\nV \u2248 297.3\u03c0
\nThe volume of the right cone is about 297.3\u03c0 in3<\/sup>.<\/p>\n
\nOscar wants to fill with water a bucket that is the shape of a right circular cylinder. It has a 6-inch radius and 12-inch height. He uses a shovel that has the shape of a right circular cone with a 3-inch radius and 4-inch height. How many shovelfuls will it take Oscar to fill the bucket up level with the top?
\nAnswer:
\nV = \u03c0r2<\/sup> h
\nV = \u03c0(6)2<\/sup> (12)
\nV = 432\u03c0
\nThe volume of the bucket is 432\u03c0 in3<\/sup>.
\nV = \\(\\frac{1}{3}\\) \u03c0r2<\/sup> h
\nV = \\(\\frac{1}{3}\\) \u03c0(3)2<\/sup> (4)
\nV = 12\u03c0
\nThe volume of shovel is 12\u03c0 in3<\/sup>.
\n\\(\\frac{432 \\pi}{12 \\pi}\\) = 36
\nIt would take 36 shovelfuls of water to fill up the bucket.<\/p>\n
\nA cylindrical tank (with dimensions shown below) contains water that is 1-foot deep. If water is poured into the tank at a constant rate of 20 \\(\\frac{\\mathrm{ft}^{3}}{\\mathrm{~min}}\\) for 20 min., will the tank overflow? Use 3.14 to estimate \u03c0.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-8th-Grade-Module-5-Lesson-10-Problem-Set-Answer-Key-5.png\")
\nAnswer:
\nV = \u03c0r2<\/sup> h
\nV = \u03c0(3)2<\/sup> (12)
\nV = 108\u03c0
\nThe volume of the tank is about 339.12 ft3<\/sup>.
\nV = \u03c0r2<\/sup> h
\nV = \u03c0(3)2<\/sup> (1)
\nV = 9\u03c0
\nThere is about 28.26 ft3<\/sup> of water already in the tank. There is about 310.86 ft3<\/sup> of space left in the tank. If the water is poured at a constant rate for 20 min., 400 ft3<\/sup> will be poured into the tank, and the tank will overflow.<\/p>\nEureka Math Grade 8 Module 5 Lesson 10 Exit Ticket Answer Key<\/h3>\n
\nUse the diagram to find the total volume of the three cones shown below.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-8-Module-5-Lesson-10-Exit-Ticket-Answer-Key-1.png\")
\nAnswer:
\nSince all three cones have the same base and height, the volume of the three cones will be the same as finding the volume of a cylinder with the same base radius and same height.
\nV = \u03c0r2<\/sup> h
\nV = \u03c0(2)2<\/sup>3
\nV = 12\u03c0
\nThe volume of all three cones is 12\u03c0 ft3<\/sup>.<\/p>\n
\nUse the diagram below to determine which has the greater volume, the cone or the cylinder.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-8-Module-5-Lesson-10-Exit-Ticket-Answer-Key-2.png\")
\nAnswer:
\nV = \u03c0r2<\/sup> h
\nV = \u03c042<\/sup> (6)
\nV = 96\u03c0
\nThe volume of the cylinder is 96\u03c0 cm3<\/sup>.
\nV = \\(\\frac{1}{3}\\) \u03c0r2<\/sup> h
\nV = \\(\\frac{1}{3}\\) \u03c062<\/sup> (8)
\nV = 96\u03c0
\nThe volume of the cone is 96\u03c0 cm3<\/sup>.
\nThe volume of the cylinder and the volume of the cone are the same, 96\u03c0 cm3<\/sup>.<\/p>\n","protected":false},"excerpt":{"rendered":"