Geo H - Chapter 11 Review
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1 Geo H - Chapter 11 Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A circle has a circumference of 50 meters. Find its diameter. a m c m b m d. 25 m 2. Write an expression for the circumference of a circle with diameter d is. a. c. b. d. 3. For a circle of radius 5 feet, find the length of an arc s with a measure of 28. a. 7 9 c b d Find the length of a 40 arc in a circle with a radius of 4. a. c. b. d. 5. An automobile has 20-inch diameter wheels. If the wheels revolved three times after the brakes were applied, the stopping distance was approximately. a ft c. 157 ft b ft d ft 6. A park has a circular swimming pool. The diameter of the pool is 19 ft. What is the distance traveled if you swim around the edge of the pool once? a. 38 ft c ft b ft d ft 7. Find the area of the shaded region. a. b. c. d. College Entrance Exam:
2 8. The figure below represents an oval track. The rounded portions of the track are semicircles. What is the length of the track? 12 ft 12 ft 106 ft a. c. b. d. 9. Write an expression for the area of a circle with diameter d. a. b. c. d. 10. In this figure, each circle has a radius of 2 inches. What is the area of the portion outside the circles but inside the square? Express your answer in terms of. a. b. c. d. 11. Find the area of an equilateral triangle with side length 14. a. b. 42 c. 98 d. 12. Find the area of a regular octagon with side length 9 cm. a c b d Find the area of a regular decagon with radius 7 cm. Round to the nearest tenth. a c b d A regular hexagon has an apothem of 2 and a side length of. Its area is.
3 a. c. b. d. 15. What is the perimeter of the regular hexagon to the nearest inch? a. 12 inches b. 24 inches c. 41 inches d. 48 inches 16. Find the number of vertices, faces, and edges for the figure below. a. 6 vertices, 6 faces, 10 edges b. 5 vertices, 6 faces, 10 edges c. 7 vertices, 7 faces, 11 edges d. 10 vertices, 6 faces, 6 edges 17. Describe the cross section. a. hexagon c. rectangle
4 b. pyramid d. triangle 18. According to Euler's Theorem, the number of faces (F), vertices (V), and edges (E) of a polyhedron is related by the formula. a. F + V = E + 2 c. F + E = V + 2 b. E + V = F + 2 d. F + V = E An aquarium in a restaurant is a rectangular prism and measures 4.5 feet by 4 feet by 2 feet. What is the volume of the aquarium? a. 32 cubic feet c cubic feet b. 36 cubic feet d cubic feet 20. Find the exact volume of a cylinder that has a height of 18 inches and a radius of 8 inches. a. 384 c. b. d. 21. Find the volume of the right triangular prism. a. 210 c. 105 b. 31 d The volume of the right prism is. a. c. 120 b. d The volume of the right circular cylinder is about.
5 a c b d The pyramid shown has a rectangular base and faces that are isosceles triangles. Find its volume. 5 ft 8 ft 6 ft a. 80 c. 34 b. 240 d Calculate the volume of the cone. Use a b. 50 c. 157 d A pyramid-shaped puzzle exactly fits its cubic storage box. The space between the puzzle and the sides of the box is filled with a light-weight plastic foam to help protect the puzzle during shipping.
6 What is the volume of the foam? a b c d Find the surface area of a sphere that has a diameter of 16 cm. Express your answer in terms of. a. 256 c b. 64 d The top of the cylindrical container shown has the shape of a hemisphere. The total volume of the container is. a. b. c. d. Numeric Response 29. GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet. The circle graph below shows the main sources of water pollution in a county.
7 What is the measure, in degrees, of the central angle of the section of the circle that represents the pollution caused by industry? 30. GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet. How many edges of a square pyramid are NOT parallel to any other edges? 31. GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet. The shaded area in the figure is a planar cross section of a cylindrical metal drum which has had the lid welded closed. Edith will cut the drum open along the edges of the cross section and add a base containing legs to make a barbecue. (The figure may not be drawn to scale.) After the drum is cut open, the cut edges must be ground to make the edges smooth. Along how many inches of metal edge must Edith grind? Short Answer 32. Find the area of the shaded region. (Assume that the ends of the figure are semicircles.)
8 33. A square is inscribed in a circle of radius. Find the area of the square. 34. A student is determining the details of a circle graph showing the results of the election for president of the student government. If 490 students voted, how many voted for Meyer? Round your answer to the nearest whole number. 35. Find the probability that a point chosen at random on is on. 36. Find the probability that a point chosen at random on is on.
9 37. A trivia game has four categories of questions. The questions are on cards colored red, blue, green, and yellow. There are a different number of questions in each category, so the game spinner that determines a player's category is divided into sectors proportional to the number of cards of each color, as shown on the spinner below. If the cards in a category are all used, then a player spinning that color loses a turn. On the first spin of the game, what is the probability that a player will be assigned a question from the blue category? Give your answer as a decimal rounded to the nearest hundredth. 38. Use Euler's Theorem to calculate how many faces a polyhedron has if it has 30 edges and 12 vertices. 39. The base of a pyramid is a regular pentagon and each of its other faces is an equilateral triangle. a. How many faces does the pyramid have? b. How many edges does the pyramid have? c. How many vertices does the pyramid have? 40. The base of a pyramid is a regular hexagon and each of its other faces is an isosceles triangle with base angles measuring 70. a. How many faces does the pyramid have? b. How many edges does the pyramid have? c. How many vertices does the pyramid have? 41. Find the volume of the rectangular prism.
10 42. Find the volume of the right prism. 43. Find the volume of the cylinder. (Round the result to one decimal place.) 44. Find the surface area and volume of the cylinder that can be folded from the net shown. 45. Find the volume of the oblique prism.
11 46. Find the volume of the right cone. Round your answer to two decimal places. 47. Find the diameter of a sphere that has a surface area of. 48. The areas of corresponding faces of two similar triangular prisms are and What is the ratio of the corresponding side lengths? of the perimeters of the corresponding faces? of the volumes? 49. The surface area of a sphere is 200. If the radius were three times as large, what would the surface area be? 50. The surface areas of two similar solids are and The volume of the larger one is What is the volume of the smaller one?
12 Geo H - Chapter 11 Review Answer Section MULTIPLE CHOICE 1. ANS: B PTS: 1 DIF: Level B REF: MHGM0102 TOP: Lesson 11.1 Circumference and Arc Length KEY: circle diameter radius circumference 2. ANS: C PTS: 1 DIF: Level A REF: HLGM1090 TOP: Lesson 11.1 Circumference and Arc Length KEY: circle diameter circumference 3. ANS: A PTS: 1 DIF: Level A REF: MGEO0025 TOP: Lesson 11.1 Circumference and Arc Length KEY: circle radius arc length 4. ANS: A PTS: 1 DIF: Level A REF: MLGE0268 TOP: Lesson 11.1 Circumference and Arc Length KEY: radius length arc 5. ANS: A PTS: 1 DIF: Level B REF: HLGM1092 TOP: Lesson 11.1 Circumference and Arc Length KEY: distance circle diameter revolution 6. ANS: B PTS: 1 DIF: Level B REF: MLGE0271 TOP: Lesson 11.1 Circumference and Arc Length KEY: word diameter circumference 7. ANS: B PTS: 1 DIF: Level A REF: MLA20277 TOP: Lesson 11.1 Circumference and Arc Length KEY: circle area sector 8. ANS: D PTS: 1 DIF: Level B REF: MIM10719 TOP: Lesson 11.1 Circumference and Arc Length KEY: word perimeter 9. ANS: D PTS: 1 DIF: Level A REF: HLGM1100 TOP: Lesson 11.2 Areas of Circles and Sectors KEY: formula circle diameter area 10. ANS: D PTS: 1 DIF: Level B REF: MGEO0032 TOP: Lesson 11.2 Areas of Circles and Sectors KEY: square circle area 11. ANS: D PTS: 1 DIF: Level A REF: OTGS0035 TOP: Lesson 11.3 Areas of Regular Polygons KEY: area triangle equilateral 12. ANS: B PTS: 1 DIF: Level B REF: PHGM1119 TOP: Lesson 11.3 Areas of Regular Polygons KEY: area polygon trigonometry regular MSC: DOK 2 NOT: ANS: B PTS: 1 DIF: Level B REF: PHGM1121 TOP: Lesson 11.3 Areas of Regular Polygons KEY: area polygon trigonometry regular MSC: DOK 2 NOT: ANS: A PTS: 1 DIF: Level B REF: MLGE0262
13 TOP: Lesson 11.3 Areas of Regular Polygons KEY: area regular hexagon apothem 15. ANS: B PTS: 1 DIF: Level B REF: 62aaf0d0-4f27-11db-b4d f7 TOP: Lesson 11.3 Areas of Regular Polygons KEY: perimeter of a regular polygon regular polygon MSC: DOK 2 NOT: ANS: A PTS: 1 DIF: Level A REF: MOT80315 TOP: Lesson 11.5 Explore Solids KEY: vertices edges faces 17. ANS: D PTS: 1 DIF: Level B REF: MGEO0034 NAT: NT.CCSS.MTH G.GMD.4 LOC: NCTM.PSSM.00.MTH.9-12.GEO.4.b NCTM.PSSM.00.MTH.9-12.MEA.2.c TOP: Lesson 11.5 Explore Solids KEY: plane three-dimension cross-section 18. ANS: A PTS: 1 DIF: Level A REF: HLGM1136 TOP: Lesson 11.5 Explore Solids KEY: Euler's Theorem vertices faces edges 19. ANS: B PTS: 1 DIF: Level B REF: TASH0033 NCTM.PSSM.00.MTH.9-12.PRS.2 KEY: volume rectangular solid prism box 20. ANS: C PTS: 1 DIF: Level B REF: MLGE0453 NAT: NT.CCSS.MTH G.GMD.3 KEY: radius surface area cone height 21. ANS: C PTS: 1 DIF: Level B REF: MLGE0318 KEY: volume prism 22. ANS: D PTS: 1 DIF: Level B REF: HLGM1171 KEY: right volume prism 23. ANS: D PTS: 1 DIF: Level B REF: HLGM1172 NAT: NT.CCSS.MTH G.GMD.3 KEY: right volume cylinder circular 24. ANS: A PTS: 1 DIF: Level B REF: MHGM0097 NAT: NT.CCSS.MTH G.GMD.3 TOP: Lesson 11.7 Volumes of Pyramids and Cones KEY: square volume pyramid 25. ANS: C PTS: 1 DIF: Level A REF: MLGE0320 NAT: NT.CCSS.MTH G.GMD.3 TOP: Lesson 11.7 Volumes of Pyramids and Cones KEY: volume cone 26. ANS: B PTS: 1 DIF: Level B REF: MC NAT: NT.CCSS.MTH G.GMD.3 TOP: Lesson 11.7 Volumes of Pyramids and Cones KEY: word composite real-life volume cube pyramid MSC: DOK 2 NOT:
14 27. ANS: A PTS: 1 DIF: Level B REF: GGEM0029 TOP: Lesson 11.8 Surface Area and Volume of Spheres KEY: diameter sphere surface area 28. ANS: B PTS: 1 DIF: Level B REF: HLGM1197 NAT: NT.CCSS.MTH G.GMD.3 TOP: Lesson 11.8 Surface Area and Volume of Spheres KEY: volume cylinder hemisphere NUMERIC RESPONSE 29. ANS: 144 PTS: 1 DIF: Level A REF: MC LOC: NCTM.PSSM.00.MTH.9-12.REP.1 TOP: Lesson 11.2 Areas of Circles and Sectors KEY: solve word data graph pie chart 30. ANS: 4 PTS: 1 DIF: Level B REF: MC LOC: NCTM.PSSM.00.MTH.9-12.REP.1 TOP: Lesson 11.5 Explore Solids KEY: square pyramid edges 31. ANS: 132 PTS: 1 DIF: Level B REF: MC LOC: NCTM.PSSM.00.MTH.9-12.REP.1 TOP: Lesson 11.5 Explore Solids KEY: word perimeter real-life cylinder cross-section SHORT ANSWER 32. ANS: PTS: 1 DIF: Level B REF: MGEO0033 TOP: Lesson 11.2 Areas of Circles and Sectors KEY: area rectangle difference semicircle 33. ANS: 36 sq. units PTS: 1 DIF: Level C REF: MLGE0284 NCTM.PSSM.00.MTH.9-12.MEA.2.c TOP: Lesson 11.2 Areas of Circles and Sectors KEY: inscribed square area 34. ANS: 253 PTS: 1 DIF: Level B REF: MC TOP: Lesson 11.2 Areas of Circles and Sectors KEY: word angle real-life sum circle graph pie chart MSC: DOK 2 NOT: ANS:
15 PTS: 1 DIF: Level A REF: MLGE0431 TOP: Lesson 11.4 Use Geometric Probability KEY: line geometric probability 36. ANS: PTS: 1 DIF: Level B REF: MLGE0432 TOP: Lesson 11.4 Use Geometric Probability KEY: line geometric probability 37. ANS: 0.21 PTS: 1 DIF: Level B REF: MC NCTM.PSSM.00.MTH.9-12.PRS.2 TOP: Lesson 11.4 Use Geometric Probability KEY: word real-life geometric probability simple MSC: DOK 2 NOT: ANS: 20 PTS: 1 DIF: Level A REF: MLGE0392 TOP: Lesson 11.5 Explore Solids KEY: Euler's Theorem vertices faces edges MSC: DOK 2 NOT: ANS: a. 6 b. 10 c. 6 PTS: 1 DIF: Level B REF: MGEO0052 TOP: Lesson 11.5 Explore Solids KEY: faces edges vertices pyramid 40. ANS: a. 7 b. 12 c. 7 PTS: 1 DIF: Level B REF: MGEO0053 TOP: Lesson 11.5 Explore Solids KEY: pyramid edges vertices faces 41. ANS: PTS: 1 DIF: Level A REF: PMG60622 KEY: volume prism 42. ANS: 825 PTS: 1 DIF: Level B REF: HLGM1167
16 43. ANS: KEY: right volume prism PTS: 1 DIF: Level B REF: HLGM1168 NAT: NT.CCSS.MTH G.GMD.3 KEY: volume cylinder 44. ANS: Area:, Volume: PTS: 1 DIF: Level B REF: HLGM1169 NAT: NT.CCSS.MTH G.GMD.3 KEY: surface cylinder area volume 45. ANS: 80 in. 3 PTS: 1 DIF: Level C REF: GEO FR.10 KEY: Free Response oblique prism volume 46. ANS: PTS: 1 DIF: Level B REF: GEO FR.12 NAT: NT.CCSS.MTH G.GMD.3 LOC: NCTM.PSSM.00.MTH.9-12.GEO.1.d NCTM.PSSM.00.MTH.9-12.MEA.2.b TOP: Lesson 11.7 Volumes of Pyramids and Cones KEY: Free Response cone volume height radius trigonometry 47. ANS: 13 in. PTS: 1 DIF: Level B REF: GGEM0095 TOP: Lesson 11.8 Surface Area and Volume of Spheres KEY: sphere surface area 48. ANS: 7:5; 7:5; 343:125 PTS: 1 DIF: Level B REF: MLGE0437 LOC: NCTM.PSSM.00.MTH.9-12.GEO.1.b NCTM.PSSM.00.MTH.9-12.MEA.2.b TOP: Lesson 11.9 Explore Similar Solids KEY: ratio area similar volume length 49. ANS: 1800 PTS: 1 DIF: Level B REF: HLGM1201 TOP: Lesson 11.9 Explore Similar Solids
17 KEY: radius area surface sphere 50. ANS: PTS: 1 DIF: Level A REF: PHGM1012 LOC: NCTM.PSSM.00.MTH.9-12.GEO.1.b TOP: Lesson 11.9 Explore Similar Solids KEY: ratio area similar volume
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