\nJay has a small fish tank. It is the same shape and size as the right rectangular prism shown in the Opening Exercise.
\na. The box it came in says that it is a 3-gallon tank. Is this claim true? Explain your reasoning. Recall that 1 gal = 231 in3<\/sup>.
\nAnswer:
\nThe volume of the tank is 715 in3<\/sup>. To convert cubic inches to gallons, divide by 231.
\n715 in3<\/sup> \u2219 \\(\\frac{1 \\text { gallon }}{231 \\mathrm{in}^{3}}\\) = 3.09 gallons
\nThe claim is true if you round to the nearest whole gallon.<\/p>\n
b. The pet store recommends filling the tank to within 1.5 in of the top. How many gallons of water will the tank hold if it is filled to the recommended level? c. Jay wants to cover the back, left, and right sides of the tank with a background picture. How many square inches will be covered by the picture? d. Water in the tank evaporates each day, causing the water level to drop. How many gallons of water have evaporated by the time the water in the tank is four inches deep? Assume the tank was filled to within Opening Exercise Exercise 1: Fish Tank Designs b. Which tank has the most surface area? Let SA(R) represent the surface area of the right rectangular prism and SA(T) represent the surface area of the right trapezoidal prism. Use your answer to fill in the blanks with SA(R) and SA(T). c. Water evaporates from each aquarium. After the water level has dropped \\(\\frac{1}{2}\\) inch in each aquarium, how many cubic inches of water are required to fill up each aquarium? Show work to support your answers. Exercise 2: Design Your Own Fish Tank Challenge: Each tank is to be constructed from glass that is \\(\\frac{1}{4}\\) in. thick. Select one tank that you designed, and determine the difference between the volume of the total tank (including the glass) and the volume inside the tank. Do not include a glass top on your tank. Question 1. Question 2. b. If the height of the container is 18 cm, how many more liters of water would it take to completely fill the container? c. What percentage of the tank is filled when it contains 2.5 L of water? Question 3. Question 4. To find the time to drain each tank, divide the capacity by the rate (liters per minute). Question 5. Question 6. Dimensions: 15 in. long by 8 in. wide by 8 in. high The first tank is less expensive. It is $1.20 cheaper.<\/p>\n Question 7. b. Jenny wants to fill each box with jelly beans. If one ounce of jelly beans is approximately 30 cm^3, estimate how many ounces of jelly beans Jenny will need to fill all four boxes? Explain your estimates. Question 8. b. Tank 2 Dimensions: 2 \\(\\frac{1}{2}\\) in. by 3 \\(\\frac{3}{4}\\) in. by 4 \\(\\frac{3}{8}\\) in. Melody is planning a raised bed for her vegetable garden. b. She needs to add soil. Each bag contains 1.5 cubic feet. How many bags will she need to fill the vegetable garden? Engage NY Eureka Math 7th Grade Module 3 Lesson 25 Answer Key Eureka Math Grade 7 Module 3 Lesson 25 Example Answer Key Example 1: Volume of a Fish Tank Jay has a small fish tank. It is the same shape and size as the right rectangular prism shown in the Opening Exercise. a. The … 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\/77382"}],"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=77382"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/77382\/revisions"}],"predecessor-version":[{"id":137779,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/77382\/revisions\/137779"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=77382"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=77382"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=77382"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nAnswer:
\nUse 8.5 in. instead of 10 in. to calculate the volume. V = 11 in \u2219 6.5 in \u2219 8.5 in = 607.75 in3<\/sup>.
\n607.75 in3<\/sup> \u2219 \\(\\frac{1 \\text { gallon }}{231 \\mathrm{in}^{3}}\\) = 2.63 gallons<\/p>\n
\nAnswer:
\nBack side area = 10 in \u2219 11 in = 110 in2<\/sup>
\nLeft and right side area = 2(6.5 in)(10 in) = 130 in2<\/sup>
\nThe total area to be covered with the background picture is 240 in2<\/sup>.<\/p>\n
\nAnswer:
\n1.5 in. of the top to start.
\nVolume when water is 4 in. deep:
\n11 in. \u2219 6.5 in. \u2219 4 in = 286in3<\/sup>
\nDifference in the two volumes:
\n607.75 in3<\/sup>-286 in3<\/sup> = 321.75 in3<\/sup>
\nWhen the water is filled to within 1.5 in of the top, the volume is 607.75 in3<\/sup>. When the water is 4 in deep, the volume is 286 in3<\/sup>. The difference in the two volumes is 321.75 in3<\/sup>. Converting cubic inches to gallons by dividing by 231 gives a difference of 1.39 gal., which means 1.39 gal. of water have evaporated.<\/p>\nEureka Math Grade 7 Module 3 Lesson 25 Exercise Answer Key<\/h3>\n
\nWhat is the surface area and volume of the right rectangular prism?
\n![\"Engage](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Engage-NY-Math-Grade-7-Module-3-Lesson-25-Exercise-Answer-Key-1.png\")
\nAnswer:
\nSurface Area = 2(11 in)(6.5 in) + 2(10 in)(6.5 in) + 2(11 in)(10 in) = 493 in2<\/sup>
\nVolume = 11 in \u2219 6.5 in \u2219 10 in = 715 in3<\/sup><\/p>\n
\nTwo fish tanks are shown below, one in the shape of a right rectangular prism (R) and one in the shape of a right trapezoidal prism (T).
\n![\"Engage](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Engage-NY-Math-Grade-7-Module-3-Lesson-25-Exercise-Answer-Key-2.png\")
\na. Which tank holds the most water? Let Vol(R) represent the volume of the right rectangular prism and Vol(T) represent the volume of the right trapezoidal prism. Use your answer to fill in the blanks with Vol(R) and Vol(T).
\n__________________ < __________________
\nAnswer:
\nVolume of the right rectangular prism: (25 in \u00d7 10 in) \u00d7 15 in = 3,750 in3<\/sup>
\nVolume of the right trapezoidal prism: (31 in \u00d7 8 in) \u00d7 15 in = 3,720 in3<\/sup>
\nThe right rectangular prism holds the most water.
\nVol(T)<\/span> < Vol(R)<\/span><\/p>\n
\n__________________ < __________________
\nAnswer:
\nThe surface area of the right rectangular prism:
\n2(25 in \u00d7 10 in) + 2(25 in \u00d7 15 in) + 2(10 in \u00d7 15 in) = 500 in2<\/sup> + 750 in2<\/sup> + 300 in2<\/sup> = 1,550 in2<\/sup>
\nThe surface area of the right trapezoidal prism:
\n2(31 in \u00d7 8 in) + 2(10 in \u00d7 15 in) + (25 in \u00d7 15 in) + (31 in \u00d7 15 in) = 496 in2<\/sup> + 300 in2<\/sup> + 375 in2<\/sup> + 555 in2<\/sup> = 1726 in2<\/sup>
\nThe right trapezoidal prism has the most surface area.
\nSA(R)<\/span> < SA(T)<\/span><\/p>\n
\nAnswer:
\nThe right rectangular prism will need 125 in3<\/sup> of water. The right trapezoidal prism will need 124 in3<\/sup> of water. First, decrease the height of each prism by a half inch and recalculate the volumes. Then, subtract each answer from the original volume of each prism.
\nNewVol(R) = (25 in)(10 in)(14.5 in) = 3,625 in3<\/sup>
\nNewVol(T) = (31 in)(8 in)(14.5 in) = 3,596 in3<\/sup>
\n3,750 in3<\/sup>-3,625 in3<\/sup> = 125 in3<\/sup>
\n3,720 in3<\/sup>-3,596 in3<\/sup> = 124 in3<\/sup><\/p>\n
\nDesign at least three fish tanks that will hold approximately 10 gallons of water. All of the tanks should be shaped like right prisms. Make at least one tank have a base that is not a rectangle. For each tank, make a sketch, and calculate the volume in gallons to the nearest hundredth.
\nAnswer:
\nThree possible designs are shown below.
\n![\"Engage](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Engage-NY-Math-Grade-7-Module-3-Lesson-25-Exercise-Answer-Key-3.png\")
\n10 gal. is 2,310 in3<\/sup>
\nRectangular Base: Volume = 2,304 in3<\/sup> or 9.97 gal.
\nTriangular Base: Volume = 2,240 in3<\/sup> or 9.70 gal.
\nHexagonal Base: Volume = 2,325 in3<\/sup> or 10.06 gal.<\/p>\n
\nAnswer:
\nHeight = 12 in-\\(\\frac{1}{4}\\) in = 11.75 in
\nLength = 24 in-\\(\\frac{1}{2}\\) in = 23.5 in
\nWidth = 8 in-\\(\\frac{1}{2}\\) in = 7.5 in
\nInside Volume = 2,070.9 in3<\/sup>
\nThe difference between the two volumes is 233.1 in3<\/sup>, which is approximately 1 gal.<\/p>\nEureka Math Grade 7 Module 3 Lesson 25 Problem Set Answer Key<\/h3>\n
\nThe dimensions of several right rectangular fish tanks are listed below. Find the volume in cubic centimeters, the capacity in liters (1 L = 1000 cm3<\/sup>), and the surface area in square centimeters for each tank. What do you observe about the change in volume compared with the change in surface area between the small tank and the extra-large tank?
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-7th-Grade-Module-3-Lesson-25-Problem-Set-Answer-Key-1.png\")
\nAnswer:
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-7th-Grade-Module-3-Lesson-25-Problem-Set-Answer-Key-2.png\")
\nWhile the volume of the extra-large tank is about five times the volume of the small tank, its surface area is less than three times that of the small tank.<\/p>\n
\nA rectangular container 15 cm long by 25 cm wide contains 2.5 L of water.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-7th-Grade-Module-3-Lesson-25-Problem-Set-Answer-Key-3.png\")
\na. Find the height of the water level in the container. (1 L = 1000 cm3<\/sup>)
\n2.5 L = 2,500 cm3<\/sup>
\nTo find the height of the water level, divide the volume in cubic centimeters by the area of the base.
\n\\(\\frac{2,500 \\mathrm{~cm}^{3}}{25 \\mathrm{~cm} \\cdot 15 \\mathrm{~cm}}\\) = 6 \\(\\frac{2}{3}\\) cm<\/p>\n
\nAnswer:
\nVolume of tank: (25 cm \u00d7 15 cm) \u00d7 18 cm = 6,750 cm3<\/sup>
\nCapacity of tank: 6.75 L
\nDifference: 6.75 L- 2.5 L = 4.25 L<\/p>\n
\nAnswer:
\n\\(\\frac{2.5 L}{6.75 L}\\) = 0.37 = 37%<\/p>\n
\nA rectangular container measuring 20 cm by 14.5 cm by 10.5 cm is filled with water to its brim. If 300 cm3<\/sup> are drained out of the container, what will be the height of the water level? If necessary, round to the nearest tenth.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-7th-Grade-Module-3-Lesson-25-Problem-Set-Answer-Key-4.png\")
\nAnswer:
\nVolume: (20 cm \u00d7 14.5 cm) \u00d7 10.5 cm = 3,045 cm3<\/sup>
\nVolume after draining: 2,745 cm3<\/sup>
\nHeight (divide the volume by the area of the base):
\n\\(\\frac{2745 \\mathrm{~cm}^{3}}{20 \\mathrm{~cm} \\times 14.5 \\mathrm{~cm}}\\) \u2248 9.5 cm<\/p>\n
\nTwo tanks are shown below. Both are filled to capacity, but the owner decides to drain them. Tank 1 is draining at a rate of 8 liters per minute. Tank 2 is draining at a rate of 10 liters per minute. Which tank empties first?
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-7th-Grade-Module-3-Lesson-25-Problem-Set-Answer-Key-5.png\")
\nAnswer:
\nTank 1 Volume: 75 cm \u00d7 60 cm \u00d7 60 cm = 270,000 cm3<\/sup>
\nTank 2 Volume: 90 cm \u00d7 40 cm \u00d7 85 cm = 306,000 cm3<\/sup>
\nTank 1 Capacity: 270 L
\nTank 2 Capacity: 306 L<\/p>\n
\nTime to drain tank 1: \\(\\frac{270 \\mathrm{~L}}{8 \\frac{\\mathrm{L}}{\\mathrm{min}}}\\) = 33.75 min.
\nTime to drain tank 2: \\(\\frac{360 \\mathrm{~L}}{10 \\frac{\\mathrm{L}}{\\mathrm{min}}}\\) = 30.6 min.
\nTank 2 empties first.<\/p>\n
\nTwo tanks are shown below. One tank is draining at a rate of 8 liters per minute into the other one, which is empty. After 10 minutes, what will be the height of the water level in the second tank? If necessary, round to the nearest minute.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-7th-Grade-Module-3-Lesson-25-Problem-Set-Answer-Key-6.png\")
\nAnswer:
\nVolume of the top tank: 45 cm \u00d7 50 cm \u00d7 55 cm = 123,750 cm3<\/sup>
\nCapacity of the top tank: 123.75 L
\nAt 8 L\/min for 10 minutes, 80 L will have drained into the bottom tank after 10 minutes.
\nThat is 80,000 cm3<\/sup>. To find the height, divide the volume by the area of the base.
\n\\(\\frac{80,000 \\mathrm{~cm}^{3}}{100 \\mathrm{~cm} \\cdot 35 \\mathrm{~cm}}\\) \u2248 22.9 cm
\nAfter 10 minutes, the height of the water in the bottom tank will be about 23 cm.<\/p>\n
\nTwo tanks with equal volumes are shown below. The tops are open. The owner wants to cover one tank with a glass top. The cost of glass is $0.05 per square inch. Which tank would be less expensive to cover? How much less?
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-7th-Grade-Module-3-Lesson-25-Problem-Set-Answer-Key-7.png\")
\nAnswer:
\nDimensions: 12 in. long by 8 in. wide by 10 in. high
\nSurface area: 96 in2<\/sup>
\nCost: \\(\\frac{\\$ 0.05}{\\mathrm{in}^{2}}\\) \u2219 96 in2<\/sup> = $4.80<\/p>\n
\nSurface area: 120 in2<\/sup>
\nCost: \\(\\frac{\\$ 0.05}{\\mathrm{in}^{2}}\\) \u2219 120 in2<\/sup> = $6.00<\/p>\n
\nEach prism below is a gift box sold at the craft store.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-7th-Grade-Module-3-Lesson-25-Problem-Set-Answer-Key-8.png\")
\na. What is the volume of each prism?
\nAnswer:
\n(a) Volume = 336 cm3<\/sup>
\n(b) Volume = 750 cm3<\/sup>
\n(c) Volume = 990 cm3<\/sup>
\n(d) Volume = 1130.5 cm3<\/sup><\/p>\n
\nAnswer:
\nDivide each volume in cubic centimeters by 30.
\n(a) 11.2 ounces
\n(b) 25 ounces
\n(c) 33 ounces
\n(d) 37.7 ounces
\nJenny would need a total of 106.9 ounces.<\/p>\n
\nTwo rectangular tanks are filled at a rate of 0.5 cubic inches per minute. How long will it take each tank to be half-full?
\na. Tank 1 Dimensions: 15 in. by 10 in. by 12.5 in.
\nAnswer:
\nVolume: 1,875 in3<\/sup>
\nHalf of the volume is 937.5 in3<\/sup>.
\nTo find the number of minutes, divide the volume by the rate in cubic inches per minute.
\nTime: 1,875 minutes.<\/p>\n
\nAnswer:
\nVolume: \\(\\frac{2625}{64}\\) in3<\/sup>
\nHalf of the volume is \\(\\frac{2625}{128}\\) in3<\/sup>.
\nTo find the number of minutes, divide the volume by the rate in cubic inches per minute.
\nTime: 41 minutes<\/p>\nEureka Math Grade 7 Module 3 Lesson 25 Exit Ticket Answer Key<\/h3>\n
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-Lesson-25-Exit-Ticket-Answer-Key-1.png\")
\na. How many square feet of wood does she need to create the bed?
\nAnswer:
\n2(4 ft)(1.25 ft) + 2(2.5 ft)(1.25 ft) = 16.25 ft2<\/sup>
\nThe dimensions in feet are 4 ft. by 1.25 ft. by 2.5 ft. The lateral area is 16.25 ft2<\/sup>.<\/p>\n
\nAnswer:
\nV = 4 ft \u2219 1.25 ft \u2219 2.5 ft = 12.5 ft3<\/sup>
\nThe volume is 12.5 ft3<\/sup>. Divide the total cubic feet by 1.5 ft3<\/sup> to determine the number of bags.
\n12.5 ft3<\/sup> \u00f7 1.5 ft3<\/sup> = 8 \\(\\frac{1}{3}\\)
\nMelody will need to purchase 9 bags of soil to fill the garden bed.<\/p>\n","protected":false},"excerpt":{"rendered":"