{"id":85030,"date":"2022-05-31T20:41:39","date_gmt":"2022-05-31T15:11:39","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=85030"},"modified":"2022-05-10T14:19:42","modified_gmt":"2022-05-10T08:49:42","slug":"eureka-math-grade-8-module-7-end-of-module-assessment","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/eureka-math-grade-8-module-7-end-of-module-assessment\/","title":{"rendered":"Eureka Math Grade 8 Module 7 End of Module Assessment Answer Key"},"content":{"rendered":"

Engage NY Eureka Math 8th Grade Module 7 End of Module Assessment Answer Key<\/h2>\n

Eureka Math Grade 8 Module 7 End of Module Assessment Task Answer Key<\/h3>\n

When using a calculator to complete the assessment, use the \u03c0 key and the full display of the calculator for computations.
\nQuestion 1.
\na. Is a triangle with side lengths of 7 cm, 24 cm, and 25 cm a right triangle? Explain.
\nAnswer:
\n72<\/sup> + 242<\/sup> = 252<\/sup>
\n49 + 576 = 625
\n625 = 625
\nYes. The lengths 7,24,25 satisfy the Pythagorean theorem, therefore, it is a right triangle.<\/p>\n

b. Is a triangle with side lengths of 4 mm, 11 mm, and 15 mm a right triangle? Explain.
\nAnswer:
\n42<\/sup> + 112<\/sup> = 152<\/sup>
\n16 + 121 = 225
\n137 \u2260 225
\nNo. The lengths 4, 11, 15 do not satisfy the Pythagorean theorem, therefore, it is not a right triangle.<\/p>\n

c. The area of the right triangle shown below is 30 ft2<\/sup>. The segment XY has a length of 5 ft. Find the length of the hypotenuse.
\n\"Engage
\nAnswer:
\n\"Engage
\n\\(\\frac{1}{2}\\) = 30
\n5h = 60
\nh = 12
\n52<\/sup> + 122<\/sup> = x2<\/sup>
\n25 + 144 = x2<\/sup>
\n169 = x2<\/sup>
\n\\(\\sqrt{169}\\) = x
\n13 = x
\nThe length of the hypotenuse is 13ft.<\/p>\n

d. Two paths from school to the store are shown below: One uses Riverside Drive, and another uses Cypress and Central Avenues. Which path is shorter? By about how much? Explain how you know.
\n\"Engage
\nAnswer:
\nLet c be the hypotenuse in miles.
\n72<\/sup> + 92<\/sup> = c2<\/sup>
\n49 + 81 = c2<\/sup>
\n130 = c2<\/sup>
\n\\(\\sqrt{130}\\) = \\(\\sqrt{c^{2}}\\)
\n\\(\\sqrt{130}\\) = c
\n11.4 \u2248 c
\nThe path along Riverside Drive is shorter, about 11.4miles, compared to the path along Cypress and Control Avenues, 16 miles. The difference is about 4.6 miles. The Pythagorean theorem allowed me to calculate the distance along Riverside Drive because the three roads from a right triangle.<\/p>\n

e. What is the distance between points A and B?
\n\"Engage
\nAnswer:
\n\"Engage
\nLet c be the distance between points A & B.
\n22<\/sup> + 52<\/sup> = c2<\/sup>
\n4 + 25 = c2<\/sup>
\n\\(\\sqrt{29}\\) = \\(\\sqrt{c^{2}}\\)
\n\\(\\sqrt{29}\\) = c
\n5.4 \u2248 c
\nThe distance between points A & B is about 5.4 units.<\/p>\n

f. Do the segments connecting the coordinates (-1, 6), (4, 2), and (7, 6) form a right triangle? Show work that leads to your answer.
\n\"Engage
\nAnswer:
\n\"Engage
\n32<\/sup> + 42<\/sup> = 52<\/sup>
\n9 + 16 = 25
\n25 = 25
\n42<\/sup> + 52<\/sup> = c2<\/sup>
\n16 + 25 = c2<\/sup>
\n\\(\\sqrt{41}\\) = \\(\\sqrt{c^{2}}\\)
\n\\(\\sqrt{41}\\) = c
\n6 < \\(\\sqrt{41}\\) < 7, So side 8 units is the longest.
\n52<\/sup> + (\\(\\sqrt{41}\\))2<\/sup> = 8 2<\/sup>
\n25 + 41 = 64
\n66 \u2260 64
\nNo. The segment connecting (-1, 6), (4, 2), and (7, 6) do not form a right triangle because their lengths do not satisfy the Pythagorean theorem.<\/p>\n

g. Using an example, illustrate and explain the Pythagorean theorem.
\nAnswer:
\nGiven a right triangle ABC, the sides a, b, c (Where c is the hypotenuse) satisfy a2<\/sup> + b2<\/sup> = c2<\/sup>
\n\"Engage
\na = 3, b = 4, c = 5
\n32<\/sup> + 42<\/sup> = 52<\/sup>
\n9 + 16 = 25
\n25 = 25<\/p>\n

h. Using a different example than in part (g), illustrate and explain the converse of the Pythagorean theorem.
\nAnswer:
\nGiven a triangle ABC with side lengths a, b, c (where c is the hypotenuse) that satisfies a2<\/sup> + b2<\/sup> = c2<\/sup>, then triangle ABC is a right triangle.
\n\"Engage
\n62<\/sup> + 82<\/sup> = 102<\/sup>
\n36 + 64 = 100
\n100 = 100
\nTherefore, triangle ABC is a right triangle because it satisfies the converse of the Pythagorean theorem.<\/p>\n

i. Explain a proof of the Pythagorean theorem and its converse.
\nAnswer:
\nSee rubric to locate proofs of the theorem and its converse within the module.<\/p>\n

Question 2.
\nDorothy wants to purchase a container that will hold the most sugar. Assuming each of the containers below can be completely filled with sugar, write a note recommending a container, including justification for your choice.<\/p>\n

Note: The figures are not drawn to scale.
\n\"Engage
\nAnswer:
\nCylinder:
\nV = 62<\/sup> \u03c0 (15)
\n= 540\u03c0<\/p>\n

\\(\\frac{1}{2}\\) Sphere:
\nV = \\(\\frac{1}{2}\\) (\\(\\frac{4}{3}\\)) \u03c0 63<\/sup>
\n= \\(\\frac{2}{3}\\) (216) \u03c0
\n= 144\u03c0<\/p>\n

Total Volume:
\n540\u03c0 + 144\u03c0 = 684\u03c0<\/p>\n

Cylinder:
\nV = 62<\/sup> \u03c0 (14)
\n= 504\u03c0<\/p>\n

Cone:
\nV = \\(\\frac{1}{3}\\)\u03c0 (62<\/sup>) 8
\n= 96\u03c0<\/p>\n

Total Volume:
\n504\u03c0 + 96\u03c0 = 600\u03c0
\nDorothy,
\nYou should choose the container with the half sphere on top because it has a greater volume than the container with the cone on top. The containers have volumes of 684\u03c0 cm3<\/sup> and 600\u03c0 cm3<\/sup>, respectively. Since 684 \u03c0 is greater than 600\u03c0, then the container with the half sphere will held more sugar compared to the container with the cone on top.<\/p>\n

Question 3.
\na. Determine the volume of the cone shown below. Give an answer in terms of \u03c0 and an approximate answer rounded to the tenths place.
\n\"Engage
\nAnswer:
\n\"Engage
\n82<\/sup> + h2<\/sup> = 152<\/sup>
\n64 + h2<\/sup> = 225
\nh2<\/sup> = 161
\n\\(\\sqrt{h^{2}}\\) = \\(\\sqrt{161}\\)
\nh = \\(\\sqrt{161}\\)
\nV = \\(\\frac{1}{3}\\) \u03c0(64) (\\(\\sqrt{161}\\))
\n= \\(\\frac{64}{3}\\) \\(\\sqrt{161}\\) \u03c0
\n\u2248 850.4
\nThe volume of the cone is exactly \\(\\frac{64}{3}\\) \\(\\sqrt{161}\\) \u03c0 mm3<\/sup> and approximately 850.4 mm3<\/sup><\/p>\n

b. The distance between the two points on the surface of the sphere shown below is 10 inches. Determine the volume of the sphere. Give an answer in terms of \u03c0 and an approximate answer rounded to a whole number.
\n\"Engage
\nAnswer:
\n\"Engage
\nx2<\/sup> + x2<\/sup> = 102<\/sup>
\n2x2<\/sup> = 100
\nx2<\/sup> = 50
\n\\(\\sqrt{x^{2}}\\) = \\(\\sqrt{50}\\)
\nx = \\(\\sqrt{50}\\)
\nV = \\(\\frac{4}{3}\\)\u03c0 (\\(\\sqrt{50}\\))3<\/sup>
\n\u2248 1481
\nThe volume of the sphere is exactly \\(\\frac{4}{3}\\)\u03c0 (\\(\\sqrt{50}\\))3<\/sup> in3<\/sup> and approximately 1481 in3<\/sup>.<\/p>\n

c. A sphere has a volume of 457 \\(\\frac{1}{3}\\) \u03c0 in3<\/sup>. What is the radius of the sphere?
\nAnswer:
\n\"Engage
\nThe radius of the sphere is 7 in.<\/p>\n","protected":false},"excerpt":{"rendered":"

Engage NY Eureka Math 8th Grade Module 7 End of Module Assessment Answer Key Eureka Math Grade 8 Module 7 End of Module Assessment Task Answer Key When using a calculator to complete the assessment, use the \u03c0 key and the full display of the calculator for computations. Question 1. a. Is a triangle with … 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\/85030"}],"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=85030"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/85030\/revisions"}],"predecessor-version":[{"id":137234,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/85030\/revisions\/137234"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=85030"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=85030"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=85030"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}