{"id":85510,"date":"2021-04-07T14:19:49","date_gmt":"2021-04-07T08:49:49","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=85510"},"modified":"2022-04-01T10:25:45","modified_gmt":"2022-04-01T04:55:45","slug":"eureka-math-grade-6-module-5-lesson-19a","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/eureka-math-grade-6-module-5-lesson-19a\/","title":{"rendered":"Eureka Math Grade 6 Module 5 Lesson 19a Answer Key"},"content":{"rendered":"

Engage NY Eureka Math Grade 6 Module 5 Lesson 19a Answer Key<\/h2>\n

Eureka Math Grade 6 Module 5 Lesson 19a Opening Exercise Answer Key<\/h3>\n

Opening Exercise:<\/p>\n

Question 1.
\nDetermine the volume of this aquarium.
\n\"Eureka
\nAnswer:
\nV = l \u00d7 w \u00d7 h
\nV = 20 in. \u00d7 10 in. \u00d7 12 in.
\nV = 2,400 in3<\/sup><\/p>\n

Eureka Math Grade 6 Module 5 Lesson 19a Mathematical Modeling Exercise Answer Key<\/h3>\n

Mathematical Modeling Exercise: Using Ratios and Unit Rate to Determine Volume<\/p>\n

For his environmental science project, Jamie is creating habitats for various wildlife including fish, aquatic turtles, and aquatic frogs. For each of these habitats, he uses a standard aquarium with length, width, and height dimensions measured in inches, identical to the aquarium mentioned in the Opening Exercise. To begin his project, Jamie needs to determine the volume, or cubic inches, of water that can fill the aquarium.<\/p>\n

Use the table below to determine the unit rate of gallons\/cubic inches.
\n\"Eureka
\nAnswer:
\n\"Eureka
\nThere are 231 cubic inches for every 1 gallon of water. So, the unit rate is 231.<\/p>\n

\u2192 Since we determined that for every gallon of water, there are 231 cubic inches, determine how many cubic inches are in the 10 gallons of water that Jamie needs for the fish.
\n\u2192 How can we determine how many cubic inches are in 10 gallons of water?
\nWe could use a tape diagram or a double number line, or we could find equivalent ratios.
\n\u2192 Using either of these representations, determine the volume of the aquarium.<\/p>\n

Determine the volume of this aquarium.
\nAnswer:
\nAnswers will vary depending on student choice. An example of a tape diagram is below.
\n\"Eureka<\/p>\n

\u2192 We determined the volume of this tank is 2,310 in3<\/sup>. This is not the same volume we calculated earlier in the Opening Exercise. Why do you think the volumes are different?
\nAnswers will vary but should include a discussion that there needs to be room for a lid; also, the water level cannot go all the way to the top so that there is room for heaters, filters, and fish, etc., without the water spilling over.<\/p>\n

\u2192 Generally, it is suggested that the highest level of water in this tank should be approximately 11.55 inches.
\nCalculate the volume of the aquarium using this new dimension.
\nV = l \u00d7 w \u00d7 h; V = 20 in. \u00d7 10 in. \u00d7 11.55 in.; V = 2,310 in3<\/sup><\/p>\n

\u2192 What do you notice about this volume?
\nThis volume is the same as the volume we determined when we found the volume using ratio and unit rates.<\/p>\n

\u2192 Let\u2019s use the dimensions 20 in. \u00d7 10 in. \u00d7 11.55 in. for our exploration.<\/p>\n

Eureka Math Grade 6 Module 5 Lesson 19a Exercise Answer Key<\/h3>\n

Optional Exercise 1:<\/p>\n

\u2192 We have determined that the volume for the 10-gallon aquarium with dimensions 20 in. \u00d7 10 in. \u00d7 11.55 in.
\nis 2,310 in3<\/sup>.
\n\u2192 Suppose Jamie needs to fill the aquarium to the top in order to prepare the tank for fish. According to our calculations, if Jamie pours 10 gallons of water into the tank, the height of the water is approximately 11.55 in.
\n\u2192 Let\u2019s test it. Begin pouring water into the aquarium 1 gallon at a time. Be sure to keep track of the number of gallons. Use a tally system.<\/p>\n

\"Eureka<\/p>\n

\"Eureka<\/p>\n

\u2192 Measure the height of the water with your ruler.
\n\u2192 What did you find about our height calculation?
\nOur calculation was correct. The height is approximately 11.55 in.<\/p>\n

Exercise 1:<\/p>\n

\"Eureka<\/p>\n

a. Determine the volume of the tank when filled with 7 gallons of water.
\nAnswer:
\n231 \\(\\frac{\\text { cubic inches }}{\\text { gallon }}\\) = 1,617 in3<\/sup>
\nThe volume for 7 gallons of water is 1,617 in3<\/sup>.<\/p>\n

b. Work with your group to determine the height of the water when Jamie places 7 gallons of water in the aquarium.
\nAnswer:
\n1,617 in3<\/sup> = (20 in. )(10 in. ) h
\n\\(\\frac{1,617 \\mathrm{in}^{3}}{200 \\mathrm{in}^{2}}=\\frac{200 \\mathrm{in}^{2}}{200 \\mathrm{in}^{2}} h\\)
\n8.085 in. = h
\nThe tank should have a water height of 8.085 inches.<\/p>\n

Optional Exercise 2:<\/p>\n

\u2192 Let\u2019s test it. Begin by pouring water into the aquarium 1 gallon at a time.
\n\u2192 Be sure to keep track of the number of gallons poured. Use a tally system.
\nOr, have students mark the height of the water using a wax marker or a dry erase marker on the outside of the tank after each gallon is poured in. Then, students measure the intervals (distance between the marks). Students should notice that the intervals are equal.
\n\u2192 Test the height at 7 gallons, and record the height measurement.<\/p>\n

\"Eureka<\/p>\n

\u2192 What did you find about our calculation?
\nOur calculation was correct. The height is about 8 inches.<\/p>\n

Exercise 2:<\/p>\n

a. Use the table from Example 1 to determine the volume of the aquarium when Jamie pours 3 gallons of water into the tank.
\nAnswer:
\nThe volume of the tank is 231 in3<\/sup> \u00d7 3 = 693 in3<\/sup>.<\/p>\n

b. Use the volume formula to determine the missing height dimension.
\n693 in3<\/sup> = 20 in.(10 in.) h
\n\\(\\frac{693 \\mathrm{in}^{3}}{200 \\mathrm{in}^{2}}=\\frac{200 \\mathrm{in}^{2}}{200 \\mathrm{in}^{2}} h\\)
\n3.465 in. = h
\nThe tank should have a water height of 3.465 in.<\/p>\n

Optional Exercise 3:<\/p>\n

\u2192 Let\u2019s test it. Begin by pouring water into the aquarium 1 gallon at a time.
\n\u2192 Be sure to keep track of the number of gallons poured. Use a tally system.
\n\u2192 Test the height at 3 gallons, and record the height measurement.
\n\"Eureka<\/p>\n

\u2192 What did you find about our calculation?
\nOur calculation was correct. The height is about 3\\(\\frac{1}{2}\\) inches.<\/p>\n

Exercise 3:<\/p>\n

a. Using the table of values below, determine the unit rate of liters to gallon.
\n\"Eureka
\nAnswer:
\n\"Eureka
\nThe unit rate is 3.785.<\/p>\n

b. Using this conversion, determine the number of liters needed to fill the 10-gallon tank. liters.
\nAnswer:
\n3.785 \\(\\frac{\\text { liters }}{\\text { gallon }}\\) \u00d7 10 gallons = 37.85 liters<\/p>\n

c. The ratio of the number of centimeters to the number of inches is 2.54: 1. What is the unit rate?
\nAnswer:
\n2.54<\/p>\n

d. Using this information, complete the table to convert the heights of the water in inches to the heights of the water in centimeters Jamie will need for his project at home.
\n\"Eureka
\nAnswer:
\n\"Eureka<\/p>\n

Exercise 4:<\/p>\n

a. Determine the amount of plastic film the manufacturer uses to cover the aquarium faces. Draw a sketch of the aquarium to assist in your calculations. Remember that the actual height of the aquarium is inches.
\nAnswer:
\nSA = (2lW) + (2lh) + (2wh)
\nSA = (2.20 in. . 10 in.) + (2.20 in. . 12 in.) + (2.10in. . 12 in.)
\nSA = 400 in2<\/sup> + 480 in2<\/sup> + 240 in2<\/sup>
\nSA = 1,120 in2<\/sup><\/p>\n

b. We do not include the measurement of the top of the aquarium since It is open without glass and does not need to be covered with film. Determine the area of the top of the aquarium, and find the amount of film the manufacturer uses to cover only the sides, front, back, and bottom.
\nAnswer:
\nArea of the top of the aquarium = l . w
\nArea of the top of the aquarium = 20 in. . 10 in.
\nArea of the top of the aquarium = 200 in2<\/sup>
\nSA of aquarium without the top = 1,120 in2<\/sup> – 200 in2<\/sup> = 920 in2<\/sup>
\n\"Eureka<\/p>\n

c. Since Jamie needs three aquariums, determine the total surface area of the three aquariums.
\nAnswer:
\n920 in2<\/sup> + 920 in2<\/sup> + 920 in2<\/sup> = 2.760 in2<\/sup> or 3920 in2<\/sup> = 2,760 in2<\/sup><\/p>\n

Eureka Math Grade 6 Module 5 Lesson 19a Problem Set Answer Key<\/h3>\n

This Problem Set is a culmination of skills learned in this module. Note that the figures are not drawn to scale.<\/p>\n

Question 1.
\nCalculate the area of the figure below.
\n\"Eureka
\nAnswer:
\nA = bh
\nA = (40 ft.) (20 ft.)
\nA = 800 ft2<\/sup><\/p>\n

Question 2.
\nCalculate the area of the figure below.
\n\"Eureka
\nAnswer:
\nA = \\(\\frac{1}{2}\\) bh
\nA = \\(\\frac{1}{2}\\) (1.3 m) (1.2 m)
\nA = 0.78 m2<\/sup><\/p>\n

Question 3.
\nCalculate the area of the figure below.
\n\"Eureka
\nAnswer:
\nArea of top rectangle:
\nA = lw
\nA = (25 in.)(12 in.)
\nA = 300 in2<\/sup><\/p>\n

Area of bottom rectangle:
\nA = lw
\nA= (7 in.)(20 in.)
\nA = 140 in2<\/sup><\/p>\n

Total Area = 300 in2<\/sup> + 140 in2<\/sup> = 440 in2<\/sup><\/p>\n

Question 4.
\nComplete the table using the diagram on the coordinate plane.
\n\"Eureka<\/p>\n

\"Eureka
\nAnswer:
\n\"Eureka<\/p>\n

Question 5.
\nPlot the points below, and draw the shape. Then, determine the area of the polygon. A(-3, 5), B(4, 3), C(0, -5)
\n\"Eureka
\nAnswer:
\n\"Eureka<\/p>\n

Area of Rectangle:
\nArea = lw
\nArea = (7 units)(10 units)
\nArea = 70 units2<\/sup><\/p>\n

Area of Triangle on Left:
\nArea = \\(\\frac{1}{2}\\)bh
\nArea = \\(\\frac{1}{2}\\)(3 units)(10 units)
\nArea = 15 units2<\/sup><\/p>\n

Area of Triangle on Top:
\nArea on top = \\(\\frac{1}{2}\\)bh
\nArea = \\(\\frac{1}{2}\\)(7 units) (2 units)
\nArea = 7 units2<\/sup><\/p>\n

Area of Triangle on Right:
\nArea = \\(\\frac{1}{2}\\)bh
\nArea = \\(\\frac{1}{2}\\)(4 units)(8 units)
\nArea = 16 units2<\/sup><\/p>\n

Total Area = 70 units2<\/sup> – 15 units2<\/sup> – 7 units2<\/sup> – 16 units2<\/sup>
\nTotal Area = 32 units2<\/sup><\/p>\n

Question 6.
\nDetermine the volume of the figure.
\n\"Eureka
\nAnswer:
\nV = l w h
\nV = (3\\(\\frac{1}{2}\\) m) (\\(\\frac{7}{8}\\) m) (1\\(\\frac{1}{4}\\) m)
\nV = \\(\\frac{245}{64}\\) m3<\/sup>
\nV = 3\\(\\frac{53}{64}\\) m3<\/sup><\/p>\n

Question 7.
\nGive at least three more expressions that could be used to determine the volume of the figure in Problem 6.
\nAnswer:
\nAnswers will vary. Some examples include the following:
\n(\\(\\frac{35}{32}\\) m2<\/sup>) (3\\(\\frac{53}{64}\\) m)
\n(1\\(\\frac{1}{4}\\) m) (\\(\\frac{7}{8}\\) m) (3\\(\\frac{1}{2}\\) m)
\n(\\(\\frac{49}{16}\\) m2<\/sup>) (1\\(\\frac{1}{4}\\) m)<\/p>\n

Question 8.
\nDetermine the volume of the irregular figure.
\n\"Eureka
\nAnswer:
\nVolume of the back Rectangular Prism:
\nV = l w h
\nV = (3\\(\\frac{5}{8}\\) ft.) (1\\(\\frac{1}{3}\\) ft) (1\\(\\frac{1}{4}\\) ft.)
\nV = \\(\\frac{580}{96}\\) ft3<\/sup><\/p>\n

Volume of the front Rectan guiar Prism:
\nV = l w h
\nV = (1\\(\\frac{1}{4}\\) ft.) (1\\(\\frac{1}{6}\\) ft.)(1\\(\\frac{1}{4}\\) ft.)
\nV = \\(\\frac{175}{96}\\) ft3<\/sup><\/p>\n

Total Volume = \\(\\frac{580}{96}\\) ft3<\/sup> + \\(\\frac{175}{96}\\) ft3<\/sup>
\n= \\(\\frac{755}{96}\\) ft3<\/sup> = 7\\(\\frac{83}{96}\\) ft3<\/sup><\/p>\n

Question 9.
\nDraw and label a net for the following figure. Then, use the net to determine the surface area of the figure.
\n\"Eureka
\nAnswer:
\n\"Eureka<\/p>\n

SA = 120 cm2<\/sup> + 84 cm2<\/sup> + 70 cm2<\/sup> + 84 cm2<\/sup> + 120 cm2<\/sup> + 70 cm2<\/sup>
\n= 548 cm2<\/sup><\/p>\n

Question 10.
\nDetermine the surface area of the figure in Problem 9 using the formula SA = 21w + 21h + 2wh. Then, compare your answer to the solution in Problem 9.
\nAnswer:
\nSA = 2lw + 2lh + 2wh
\nSA = 2(10 cm)(7 cm) + 2(10 cm)(12 cm) + 2 (7 cm)(12 cm)
\nSA = 140 cm2<\/sup> + 240 cm2<\/sup> + 168 cm2<\/sup>
\nSA= 548 cm2<\/sup><\/p>\n

The answer in Problem 10 is the same as in Problem 9. The formula finds the areas of each pair of equal faces and adds them together, like we did with the net.<\/p>\n

Question 11.
\nA parallelogram has a base of 4.5 cm and an area of 9.495 cm2<\/sup>. Tania wrote the equation 4.5x = 9.495 to represent this situation.<\/p>\n

a. Explain what x represents in the equation.
\nAnswer:
\nx represents the height of the parallelogram in centimeters.<\/p>\n

b. Solve the equation for x and determine the height of the parallelogram.
\nAnswer:
\n\\(\\frac{4.5 x}{4.5}=\\frac{9.495}{4.5}\\)
\nx = 2.11
\nThe height of the parallelogram is 2.11 cm.<\/p>\n

Question 12.
\nTriangle A has an area equal to one-third the area of Triangle B. Triangle A has an area of 3\\(\\frac{1}{2}\\) square meters.<\/p>\n

a. Gerard wrote the equation \\(\\frac{B}{3}\\) = 3\\(\\frac{1}{2}\\). Explain what B represents in the equation.
\nAnswer:
\nB represents the area of Triangle B in square meters.<\/p>\n

b. Determine the area of Triangle B.
\nAnswer:
\n\\(\\frac{B}{3}\\) . 3 = 3\\(\\frac{1}{2}\\) . 3
\nThe area of Triangle is 10\\(\\frac{1}{2}\\) square meters.<\/p>\n

Eureka Math Grade 6 Module 5 Lesson 19a Exit Ticket Answer Key<\/h3>\n

Question 1.
\nWhat did you learn today? Describe at least one situation in real life that would draw on the skills you used today.
\nAnswer:
\nAnswers will vary.<\/p>\n","protected":false},"excerpt":{"rendered":"

Engage NY Eureka Math Grade 6 Module 5 Lesson 19a Answer Key Eureka Math Grade 6 Module 5 Lesson 19a Opening Exercise Answer Key Opening Exercise: Question 1. Determine the volume of this aquarium. Answer: V = l \u00d7 w \u00d7 h V = 20 in. \u00d7 10 in. \u00d7 12 in. V = 2,400 … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/85510"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=85510"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/85510\/revisions"}],"predecessor-version":[{"id":91381,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/85510\/revisions\/91381"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=85510"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=85510"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=85510"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}