Geometry B Practice Exam

Transcription

1 Geometry B Practice Exam Name 1. The lengths (in inches) of two sides of a regular octagon are represented by the expressions and. Find the length of a side of the octagon. 2. Circular disks with a diameter of 10 inches are stamped out of a square sheet of metal as shown below. How many square inches of waste sheet metal are left after the disks are stamped out? Use 3.14 as an approximation for 3. The ratios of the side lengths of triangle ABC are 7:9:12 (AB:AC:BC). Solve for x. 4. Solve the proportion. 5. A board 24 inches long is cut into two pieces in the ratio Find the length of each piece. 6. The measures of the angles of a triangle are in the extended ratio of 7 : 9 : 10. Find the measures of the angles of the triangle. 7. Given that, find AB to the nearest tenth. The figure is not drawn to scale.

2 a b c d Given that ABC DEF, solve for x and y. 9. Triangle ABC is similar to triangle DEF. The perimeter of is 108 centimeters. What is the length of 10. True or false: triangle ABC is similar to triangle DEF.

3 Determine whether the triangles are similar. If the are, write a similarity statement In and In and State whether the triangles are similar, and if so, write a similarity statement. Tell whether each pair of triangles is similar. Explain your reasoning Given:. Find the length of.

4 17. Find the area of this right triangle if and 18. Find the area of the isosceles triangle with side lengths 14 inches, 25 inches, and 25 inches. 19. Classify a triangle with sides 10, 10, and 9 as acute, obtuse, or right. 20. Find the value of x and y. 21. A photographer shines a camera light at a particular painting forming an angle of 47 with the camera platform. If the light is 52 feet from the wall where the painting hangs, how high above the platform is the painting?

5 a ft b ft c ft d ft 22. Use the diagram to find sin x as a fraction in simplest form. a. c. b. d. 23. Find the missing side lengths for x and y. 24. Solve using the diagram and the given measurements. (Note: The triangle is not drawn to scale.) B = 43, a = Solve for x to the nearest degree.

6 a. 72 b. 71 c. 18 d Two legs of a right triangle have lengths 15 and 8. The measure of the smaller acute angle is. a b. 17 c d Find the measure of an acute angle that satisfies the given equation. Round your answers to the nearest tenth of a degree Find the value of x. 29. Find the number of sides of a regular polygon with each interior angle equal to. 30. What is the measure of each exterior angle in a regular pentagon? Find the value of x. (The figure may not be drawn to scale.)

7 31. a. 66 b. 116 c. 62 d. 64 Use the diagram. 32. Segment is translated by the rule (x, y) (x 4, y + 5). Find the coordinates of the endpoints of the image. 33. The rule for this transformation of onto is.

8 a. (x, y) (x 9, y 2) c. (x, y) (x 9, y + 2) b. (x, y) (x + 9, y + 2) d. (x, y) (x + 9, y 2) 34. The translation vector is = The image of point A is Find the coordinates of A. 35. The vertices of are. Reflect the triangle in the line. Graph the triangle and its image. 36. Graph the figure with vertices, and Rotate the figure 180 about the origin. 37. Find the coordinates of the image of a triangle with vertices A(0, 2), B(4, 0), and C(2, 8) for a rotation of 270 counterclockwise about the origin. 38. Name the transformation. (Preimages are unshaded; images are shaded.) 39. In the diagram, the quadrilateral is rotated about P. What is the value of y?

9 40. Point A is reflected over line m, then its image,, is reflected over line n, which is parallel to line m, to create a second image, point A?. How far is point A from point A?, in centimeters? (The figure may not be drawn to scale.) 41. Each triangle is an image of. Which triangle is the image of after a reflection over line r and then a reflection over line s? Graph with vertices Then graph its image after the given transformation. 42. Translate using Then rotate Which of the following letters (if drawn as simply as possible) has at least one line of symmetry? Q, S, T, Z a. S b. T c. Q d. Z 44. Which figure shows all lines of symmetry?

10 a. c. b. d. 45. State whether the following figure has line symmetry, rotational symmetry, both kinds of symmetry, or neither kind of symmetry. 46. Does the figure have line symmetry, rotational symmetry, or both? Tell what type of transformation is described.

11 47. The coordinates of the image are four times the corresponding coordinates of the original. 48. Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement. 49. Find the area of the shaded triangle. 50. The area of a regular octagon is What is the area of a regular octagon with sides three times as large as the sides of the first octagon? a. c. b. d. 51. Leila needs to make a poster that is 2 m by 3.5 m for the big game. The cost of the paper is $2.75. Later she needs another poster with dimensions 1 m by 1.75 m. What is the paper for this poster likely to cost? a. $0.44 c. $1.38 b. $0.69 d. $ If both the base and height of a triangle are made nine times as long, how many times the area of the original figure is the area of the new figure? a. nine times c. eighty-one times b. ninety times d. thirty-six times 53. A circle has a circumference of 37 meters. Find its diameter. a m c m b m d m

12 54. An expression for the circumference of a circle with diameter d is. a. c. b. d. 55. The circumference of a circle is Find the diameter, the radius, and the length of an arc of. 56. Find the length of a 40 arc in a circle with a radius of 4. a. c. b. d. 57. Find the arc length of to two decimal places. College Entrance Exam: 58. The figure below represents an oval track. The rounded portions of the track are semicircles. What is the length of the track? a. c. b. d. 59. Find the area of the shaded region. Express your answer in terms of.

13 60. 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. 61. Find the area of the shaded sector in terms of 62. Find the area of the shaded sector to the nearest whole number. 63.

14 64. The rectangular part of the field below is 140 yards long, and the diameter of each semicircle is 40 yards. Find the cost of reseeding the field at $0.70 per square yard. 65. Each circle is tangent to the other two. If the diameter of the large circle is 12, the area of the shaded region is. a. c. b. d. 66. The perimeter of an equilateral triangle is 18. Find its area. 67. Find the area of a regular pentagon with radius 6 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. a. c. b. d.

15 69. What is the perimeter of the regular hexagon to the nearest inch? a. 12 inches b. 24 inches c. 41 inches d. 48 inches 70. A polyhedron has 6 faces and 7 vertices. How many edges does it have? Explain your answer. 71. What is the sum of the number of faces, the number of vertices and the number of edges in a square pyramid? 72. Find the surface area of the triangular prism. a cm 2 c cm 2 b cm 2 d. 271,814.4 cm 2

16 73. The figure shown is a cylindrical solid with a circular cylindrical hole drilled out of the center. Find the surface area of the resulting solid. 74. Find the surface area of the right cylinder below. (Round the result to two decimal places.) 75. Calculate the surface area of the lateral faces of a regular octagonal pyramid that has a slant height of 33 cm and a base side length of 76. Find the surface area of the lateral faces on the regular pyramid below. a. 336 c. 168 b. 532 d A regular pyramid has a base area of in. Its surface area is. a. c. b. d., a base perimeter of 12 in., and a slant height of

17 78. A pyramid is in the form of a regular tetrahedron of edge length 2 in. Find its surface area. 79. Find the area of the lateral surface of a cone with height of 16 cm and radius of 30 cm. Express the answer in terms of. 80. The box shown is a candy container with a square base and a pyramidal top. How many square inches of pasteboard are need to make the box, not counting any overlapping edges? a. 96 square inches c square inches b. 112 square inches d. 144 square inches 81. Find the lateral area of a right cone with height 12 inches and radius 5 inches. Round your answer to two decimal places. 82. Find the volume of the rectangular prism. 83. Find the exact volume of a cylinder that has a height of 17 inches and a radius of 8 inches. a. c.

18 b. d. 84. Which has a greater volume: a cube with edge length x or a cylinder with height of x and diameter of x? Explain. 85. Find the volume of the right prism. 86. Find the surface area and volume of the cylinder that can be folded from the net shown. 87. A concrete block has a cylindrical hole 4 feet in diameter drilled through it to allow a pipe to pass through. Use 3.14 as an approximation for and round your answer to the nearest tenth. How many cubic feet of concrete are left in the block? a cubic feet c cubic feet

19 b cubic feet d cubic feet 88. The volume of a right cylinder is and the height is 10 cm. Find the diameter. 89. The pyramid shown has a rectangular base and faces that are isosceles triangles. Find its volume. a. b. c. 80 d Find the volume of a right cone with slant height of 34 cm and radius of 16 cm. Express in terms of. 91. Describe what happens to the volume of a cone if its radius is doubled while its height is halved. The volume is. a. unchanged b. doubled c. increased by a factor of d. not able to be determined 92. A machinist drilled a conical hole into a cube of metal as shown. If the cube has sides of length 8 cm, what is the volume of the metal after the hole is drilled? and round to the nearest tenth.

20 a b c d Find the diameter of a sphere that has a surface area of. 94. Find the surface area to the nearest tenth of a square inch of a sphere that has a radius of 17.3 inches. 95. A company has a spherical storage tank which is in need of painting. The radius of the tank is 35.4 ft. The type of paint used will cover approximately 160 per gallon. How many gallons of paint will be needed? (Round decimal to the higher whole number of gallons.) 96. The inside of an ice cream cone is filled with ice cream and has radius and height Assuming that a half-scoop of ice cream is in the shape of a hemisphere, and that it fits perfectly on top of the cone (same radius), find the total volume of ice cream. Use 3.14 for and round your answer to the nearest tenth. a. b. c. d. 97. The top of the cylindrical container shown has the shape of a hemisphere. The total volume of the container is. a.

21 b. c. d. 98. A sphere fits snugly inside a right cylinder as shown below. Find the volume lying outside the sphere but inside the cylinder to the nearest tenth of a cubic inch. Performance Task: 99. Three balls are packaged in a cylindrical container as shown below. If the balls just touch the top, bottom, and sides of the cylinder, how much of the space inside the cylinder is not filled by the balls if the diameter of a single ball is 9 cm? Justify each step in your solution 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? 101. The surface area of a sphere is 200. If the radius were three times as large, what would the surface area be? 102. The surface areas of two similar solids are and The volume of the larger one is What is the volume of the smaller one? 103. If the radius of a sphere is halved, what fraction of the original volume is the new volume?

22 Decide whether the solids are similar