Geometry 2 Final Review

Transcription

1 Name: Period: Date: Geometry 2 Final Review 1 Find x in ABC. 5 Find x in ABC. 2 Find x in STU. 6 Find cos A in ABC. 3 Find y in XYZ. 7 Find x to the nearest tenth. 4 Find x in HJK. 8 Find the angle of elevation of the sun when a pole 25 feet tall casts a shadow 42 feet long. 9 Find the geometric mean between 7 and 12. 1

2 10 Find x. 15 Find x to the nearest degree. 11 Find y. 16 If a 20-foot ladder makes a 65 angle with the ground, how many feet up a wall will it reach? Round your answer to the nearest tenth. 12 Find x. 17 Given A(3, 7), under which reflection is A (3, 7)? A reflection in the x-axis B reflection in the y-axis C reflection in the origin D reflection in the line y = x 18 Find the magnitude of the rotational symmetry in a regular pentagon. 13 Find c. 19 Find the coordinates of X with X(-6, 5) for a dilation centered at the origin with a scale factor of Find the perimeter of a square if the length of its diagonal is 12 inches. Round to the nearest tenth. 20 Given B( 4, 6), under which reflection is B (4, 6)? A reflected in the x-axis B reflected in the y-axis C reflected in the origin D reflected in the line y = x 2

3 21 Name the image of EF under reflection in. FH 26 Find the image of AB with A( 3, 1) and B( 1, 5) under a rotation of 90 clockwise about the origin. A B C D FG HG EH FE 27 Find the measure of the image of ST if ST = 4 under a dilation with a scale factor of Find the scale factor if D E F is the image of DEF under a dilation with center C. 28 If ST = 12 and S T = 9, find the scale factor of the dilation. 29 Given ABC with vertices A(1, 0), B(6, 7), and C(0, 4). Find the coordinates of the vertices of the triangle under the translation (x, y) ( x, y 4). 30 In C, mab = 72. Find m BCD. 23 Find the reflection of the point A(6, 1) across the line y = x. 24 Write the coordinates of the image of P( 2, 5) reflected in the line y = x. 31 Find the length of PQ in R to the nearest hundredth. 25 Find the image of WX with W(7, 1) and X( 4, 5) under the translation (x, y) (x 4, y 3). 3

4 32 In O, AB = 12 centimeters, OE = 4 centimeters, and OF = 4 centimeters. Find CF. 37 Find z. 38 Find x. 33 Find the radius of a circle if a 48-meter chord is 7 meters from the center. 34 Find m ABC. 39 Identify the graph of (x 3) 2 + (y + 2) 2 = 4. A 35 Find x. B C 36 Find y. D 4

5 40 Find x. 45 Find the radius of O if DE = 12 inches and DE bisects OF. 41 The diameter of a circular swimming pool is 15 feet. Find the circumference to the nearest hundredth. 46 Find x. 42 In A, m BAD = 110. Find mde. 47 EFGH is a quadrilateral inscribed in P with m E = 72 and m F = 49. Find m G. 43 Points X and Y lie on P so that PX = 5 meters and m XPY = 90. Find the length of XY to the nearest hundredth. 48 If AB is tangent to C at A, find BC. 44 Chords XY and WV are equidistant from the center of O. If XY = 2x + 30 and WV = 5x 12, find x. 5

6 49 PQ, QR, RS, and SP are tangent to X. Find the perimeter of PQRS. 54 Find the equation of P. 50 Find x. 55 Find YB if the diameter of A is 10 inches, the diameter of B is 8 inches, and AX = 3 inches. 51 Find y. 56 In K, m HKG = x + 10 and m IKJ = 3x 22. Find mfj. 52 Find z. 57 The diameter of C is 18 units long. Find the length of an arc that has a measure of 100. Round to the nearest hundredth. 53 Find the center of the circle whose equation is (x + 11) 2 + (y 7) 2 =

7 58 In A, CG = 5x + 2 and GD = 7x 12. Find x. 62 Find x if BA is tangent to P at A. 59 In O, PQ = 18 meters. Find the distance from O to PQ. 63 Write the equation of a circle with a diameter having endpoints at ( 2, 6) and (8, 4). 64 Write the equation of a circle with a radius of 10 and a center at ( 4, 9). 60 Find x. 65 Find the area of parallelogram WXYZ. Round to the nearest tenth. 61 Find x. 66 Find the area of quadrilateral DEFG. 7

8 67 Find the area of a regular octagon with a perimeter of 96 centimeters. 73 Find the area of a nonagon with a perimeter of 126 inches. Round to the nearest tenth. 68 Find the area of an equilateral triangle with a side length of 14 inches. 74 Find the area of the shaded region. Round to the nearest tenth. 69 Find the probability that a point chosen at random lies in the shaded sector. 75 A running track consists of two parallel lines that are connected at each end by the curved boundary of a semicircle. The parallel lines are 30 meters long and 7 meters apart. Find the area of the running track. 70 Find the area of the shaded segments. 76 Find the probability that a point chosen at random lies in the shaded region. 71 A rhombus has an area of 165 square units. If the length of one of its diagonals is 15 units, find the length of its other diagonal. Find the area of each parallelogram. Round to the nearest tenth if necessary. 72 Find the area of a regular hexagon with side length of 10 centimeters. Round to the nearest tenth. 77 8

9 78 The area of parallelogram ABCD is 2250 square meters. Find the lengths of the height and base. 83 Find the surface area of a rectangular prism with a length of 8 inches, a width of 5 inches, and a height of 2 inches. 84 The lateral area of a regular pyramid is 300 square units. The perimeter of its base is 100 units. Find the slant height of the pyramid. Find the area of each polygon. Round to the nearest tenth. 79 a square with a perimeter of 16 2 inches Refer to the figure. 80 a regular hexagon with apothem length of 4.3 centimeters 85 Find the lateral area. 81 A children s game is won by tossing a coin so that it lands on the white part of this board. If one coin is tossed, what is the probability of winning? 86 The radius of a cone is 17 inches long and the slant height is 20 inches. Find the surface area to the nearest tenth. 87 The diameter of a sphere is 42 centimeters. Find the surface area to the nearest tenth. 82 If the length of the height of a trapezoid is 4 meters, the length of one of its bases is 11 meters, and its area is 62 square meters, then what is the measure of the other base? 9

10 88 Find the surface area of the prism. Refer to the figure. Round to the nearest tenth. 93 Find the lateral area. 89 The surface area of a right cylinder is 200π square centimeters and the radius is 4 centimeters. Find the height of the cylinder. 94 Find the surface area to the nearest tenth. Use a right cylinder with a radius of 3 inches and a height of 17 inches. Round to the nearest tenth. 95 Find the surface area of the solid. 90 Find the lateral area. 91 Find the surface area. 96 Find the lateral area of a right cylinder with a diameter of 8.6 yards and a height of 19.4 yards. Round to the nearest tenth. Refer to the figure. 97 Find the lateral area of the triangular pyramid. 92 Find the surface area. 10

11 98 The surface area of a regular pyramid is 276 square centimeters, the slant height measures 8 centimeters, and the area of the base is 50 square centimeters. Find the perimeter of the base. 103 Find the volume of the oblique cone. Round to the nearest tenth. 99 Plane A intersects sphere R in X. Find the radius of the sphere. 104 A sphere has a radius that is 12 centimeters long. Find the volume of the sphere. Round to the nearest tenth. 100 Find the surface area of this hemisphere to the nearest tenth. 105 A sphere has a volume that is 36π cubic meters. Find the radius of the sphere. 106 A cylinder whose height is 5 meters has a volume of 320π cubic meters. Find the radius of the cylinder. 101 The volume of a cylinder is 62.8 cubic meters and the radius is 2 meters. Find the height of the cylinder. Round to the nearest meter. 107 A square pyramid has a height that is 8 centimeters long and a base with sides that are each 9 centimeters long. Find the volume of the pyramid. 102 Find the volume of the pyramid. 108 The volume of a cone is 1080π cubic centimeters and the radius is 18 centimeters. Find the height of the cone. 11

12 109 Find the volume to the nearest tenth. 115 A regular hexagonal pyramid has a height that is 15 feet and a base 6 feet on each side. Find the volume of the pyramid. 110 A sphere has a volume of 972π cubic inches. Find the radius of the sphere. 116 The volume of a pyramid is 120 cubic inches and the area of the base is 50 square inches. Find the height of the pyramid. 111 The ratio of the radii of two similar cylinders is 3:5. The volume of the smaller cylinder is 54π cubic centimeters. Find the volume of the larger cylinder. 117 The surface area of a sphere is square inches. Find the volume of the sphere. Round to the nearest cubic inch. 118 Find the volume of the solid. Round to the nearest tenth. 112 The ratio of the heights of two similar solids is 7:9. Find the ratio of their volumes. 113 A box has a length of 12 inches, a width of 9 inches, and a height of 4 inches. Find the volume of the box. 114 Find the volume of the cylinder. Round to the nearest tenth. 119 The ratio of the heights of two similar prisms is 2:7. The surface area of the smaller prism is 50 square meters. Find the surface area of the larger prism. 120 The ratio of the volumes of two similar solids is 8:27. Find the ratio of their surface areas. 12