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Review 9 - Charles S. Rushe Middle School

Name Date ClassCHAPTER9**Review**Volume and Surface Area, continued9-4 Surface Area of Prisms, Cylinders, and Spheres(pp. 486–490)Find the surface area of the prism to the nearest tenth.13. 14. 15.13 in. 15 in.6 ft15 in.4 ft10.2 m8 ft8.4 in.15 in.17.4 m8.9 mFind the surface area of the cylinder to the nearest tenth using3.14 for .16. 7.6 in.17. 18 mm18.42 cm10.7 in.34 mm46 cmFind the surface area of the sphere to the nearest tenth using3.14 for .19. 20. 21.12 cm6.3 cm12.9 in.9-5 Changing Dimensions (pp. 491–495)Given the scale factor, find the surface area of the similar prism.22. The scale factor of two similar rectangular prisms is 8.The surface area of the smaller prism is 64 ft 2 .Given the scale factor, find the volume of the larger prism.23. The scale factor of two similar hexagonal prisms is 9.The volume of the smaller prism is 9.4 m 3 .Copyright © by Holt, Rinehart and Winston.55 Holt **Middle** **School** Math Course 2All rights reserved.

LESSON9-5ChallengeEggs-actlyThe volumes of two similar-shaped figuresare proportional to the cube of their lengths.Suppose an extra-large egg is 2.5 inches long,compared to a smaller egg 1.25 inches long.What is the ratio of their volumes?Cube the ratio of their lengths. 2.51.25 3 2 1 3 8 1 The ratio of their volumes is 8:1.So, the larger egg has 8 times as much volume, 8 times as muchweight, and 8 times as much food.Solve. Show your work.1. One egg is 2 inches long. Another is 2.75 inches long. Howmany times greater is the volume of the larger egg? 2. 752 3 20.8 2.6; about 2.6 times82. One egg is 2.25 inches long. Another is 1.5 inches long. Howmany times greater is the weight of the larger egg? 2 . 2531.5 3 2 3 about 3.4 times3. The ratio of the lengths of two eggs is 5 to 2. The larger eggcontains how many times the food of the smaller egg?5 15.625; about 15.6 times as much 5 2 3 12 84. An egg is 2 inches long. What is the approximate length of anegg with twice the volume?about 2.5 in.5. An egg is 3 inches long. What is the approximate length of anegg with half the weight?about 2.4 in.6. An egg is 1.75 inches long. What is the approximate length of anegg with twice the food?about 2.2 in.2.5 in.1.25 in.LESSON9-5Problem SolvingChanging DimensionsWrite the correct answer.1. In the late 1800s, wax cylinders wereused to record sound. The lateralsurface area of the cylinders wasabout 25 square inches. If a largermodel of this cylinder is createdusing a scale factor of 3, what is thelateral surface area of the model?about 225 in 23. A cone-shaped plastic cup holds24 ounces of water. A smaller cuphas a scale factor of 1 . How much2water does the smaller cup hold?3 ozChoose the letter of the correct answer.2. A 5-foot wide, 100-foot tall cylindricalwater tower was built in St. Louis inthe early 1800s. An architecturestudent wants to build a model usinga scale factor of 1 . What will be the6volume of the model to the nearestcubic foot?9 ft 34. In the game of Ring Taw, players usea shooting marble that has a surfacearea of 1.77 square inches. What isthe surface area of a large ball if thescale factor is 5?44.25 in 26. A cooking pot used in the cafeteria5. The volume of a rectangular prism isB 0.026 mi 2 D 0.126 mi 248 cubic centimeters. The volume ofa similar rectangular prism is 6 cubicweighs 64 pounds when it is filledwith soup. How much would a similarcentimeters What is the scale factor pot with a scale factor of 1 2 for the rectangles?when filled with the same soup?A 8 C 4F 4 lbH 16 lbB 6 D 2G 8 lb J 32 lb7. For his science project, Marty isbuilding a model of Pluto, whichhas a surface area of about6,376,000 square miles. He plans to8. The scale factor of two similartriangular prisms is 5. What is thepossible surface area of both prisms?F 2,000 cm 2 and 80 cm 2cover his model with red foil. If heG 125 cm 2 and 25 cm 2uses a scale factor of 5,000, howmuch red foil will he need to theH 5,000 cm 2 and 40 cm 2nearest hundredth of a square mile? J 10,000 cm 2 and 60 cm 2A 1.26 mi 2 C 0.26 mi 2Copyright © by Holt, Rinehart and Winston.51 Holt **Middle** **School** Math Course 2All rights reserved.Copyright © by Holt, Rinehart and Winston.52 Holt **Middle** **School** Math Course 2All rights reserved.LESSON9-5Puzzles, Twisters & TeasersA New Dimension!9-1 Introduction to Three-Dimensional Figures (pp. 472–475)560 in 2Complete both charts. Use your answers to solve the riddle.4 35 in 2 T 2 29 ft 3 232 ft 3 CIdentify the type of base of each prism or pyramid. Then tell thescale smaller larger scale smaller largername of the prism or pyramid.factor surface area surface area factor volume volume 1. 2. 3.6 24 m 2 864 m 2 S8 40 ft 2 2,560 ft 2 U9 20 m 2 H 1.602 m 2Why did the hairdresser win the race?S H E T O O K A864 20 486 560 1,088 1,088 75 2,048S H O R T C U T .864 20 1,088 1,000 560 232 2,560 5603 18 lb 3 486 lb 3 E5 8 cm 3 1,000 cm 3 R4 17 in 3 1,088 in 3 O4 32 lb 3 2,048 lb 3 A2 75 in 3 K 600 in 3CHAPTER9**Review**Volume and Surface Areatriangle;triangular prismoctagon;octagonal prism9-2 Volume of Prisms and Cylinders (pp. 476–479)Find the volume of the prism to the nearest tenth.4. 5. 3 m6.5.1 m3.4 m9 m15 in.7.2 m12 m15 in.15 in.124.8 m 3 162 m 33,375 in 3Find the volume of the cylinder to the nearest tenth using 3.14 for .triangle;triangular pyramid15.6 cm7. 10 cm8.18 m9.5,338 cm 3 32,555.5 m 31,413.7 cm 317 cm7.4 cm32 m9-3 Volume of Pyramids, Cones, and Spheres (pp. 480–484)Find the volume of the pyramid, cone, and sphere to the nearest tenth.Use 3.14 for .10. 11. 12.16 in.5.2 cm6 in.8 in. 15 in.3 in.640 in 3 56.5 in 3588.7 cm 3Copyright © by Holt, Rinehart and Winston.53 Holt **Middle** **School** Math Course 2All rights reserved.Copyright © by Holt, Rinehart and Winston.54 Holt **Middle** **School** Math Course 2All rights reserved.Copyright © by Holt, Rinehart and Winston.70 Holt **Middle** **School** Math Course 2All rights reserved.

CHAPTER9**Review**Volume and Surface Area, continued9-4 Surface Area of Prisms, Cylinders, and Spheres(pp. 486–490)Find the surface area of the prism to the nearest tenth.13. 14. 15.13 in. 15 in.6 ft15 in.4 ft10.2 m8.9 m8 ft8.4 in.15 in.17.4 m144 ft 2 573 in 2846.2 m 2Find the surface area of the cylinder to the nearest tenth using3.14 for .42 cm16. 7.6 in.17. 18 mm18.873.4 in 2 5,878.1 mm 28,836.0 cm 210.7 in.34 mm46 cmFind the surface area of the sphere to the nearest tenth using3.14 for .19. 20. 21.12 cm6.3 cm12.9 in.1,808.6 cm 2 498.5 cm 2522.5 in 29-5 Changing Dimensions (pp. 491–495)Given the scale factor, find the surface area of the similar prism.22. The scale factor of two similar rectangular prisms is 8.The surface area of the smaller prism is 64 ft 2 .Given the scale factor, find the volume of the larger prism.4,096 ft 223. The scale factor of two similar hexagonal prisms is 9.The volume of the smaller prism is 9.4 m 3 . 6,852.6 m 3CHAPTER9Project Recording SheetPyramid SchemeThe pyramids of the ancient world inspire our imaginations. How andwhy did people who lived so long ago create such majestic buildings?Use the formula for a pyramid, V 1 Bh, to complete the chart.3Length of Side VolumePyramid Who Location Height (m) of Base (m) (m 3 )Chichen Itza,El Castillo Toltecs Mexico 55.5 79.0 115,458Tikal Mayans Guatemala 30.0 80.0 64,000Pyramid ofTeotihuacan,the Sun Aztecs Mexico 63.0 225.0 1,063,125Great PharaohPyramid Khufu Giza, Egypt 146.5 230.38 2,591,826Khafre’s PharaohPyramid Khafre Giza, Egypt 143.5 215.25 2,216,241Menkaure’s PharaohPyramid Menkaure Giza, Egypt 66.45 104.6 242,3471. Does the tallest pyramid have the greatest volume? Why do youthink the result is the way it is?Yes, because the tallest pyramid also has the base with the greatest area.2. Does the tallest pyramid have the greatest surface area? Whydo you think the result is the way it is?Yes, the lengths of all the sides of the tallest pyramid are the greatest.Research: When was the Great Pyramid built?Around 2500 B.C. and was the tallest building on earth for 4,500 yearsWhat were the reasons the pyramids were built?Possible answer: They were built to house the kings and theirpossessions after death.Extension: Construct a model of one of the pyramids. Use what youknow about scale models to make sure that you can relate it to thefull-size pyramid.Copyright © by Holt, Rinehart and Winston.55 Holt **Middle** **School** Math Course 2All rights reserved.Copyright © by Holt, Rinehart and Winston.56 Holt **Middle** **School** Math Course 2All rights reserved.Copyright © by Holt, Rinehart and Winston.71 Holt **Middle** **School** Math Course 2All rights reserved.