Geometry Test Review. π. a. A = π cm cm 2 b. A = 63.2π cm cm 2 c. A = 31.6π cm cm 2 d. A = π cm

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1 Name: _ Date: Period: _ Score: Geometry Test Review 1. The distance between two cities is 600 miles. On a map, they are 4 inches apart. What is the scale of the map? a. 4 in.:100 mi b. 1 in.:600 mi c. 1 mi:150 in. d. 1 in.:150 mi 2. The height of a tower on a scale drawing is 18 centimeters. The scale is 2 cm:19 m. What is the actual height of the tower? a. 342 m b. 171 m c. 684 m d. 36 m 3. Which of the following describes the vertical cross section of the right rectangular pyramid shown that contains the vertex of the pyramid and the midpoints of the sides of the base that are 8 yards long? a. A rectangle with dimensions 8 yards by 12 yards b. A rectangle with dimensions 12 yards by 14 yards c. An isosceles triangle with base 8 yards and height 14 yards d. An isosceles triangle with base 12 yards and height 14 yards 4. Find the measure of an angle whose complement is two times the measure of the angle. a b. 30 c. 60 d Name an angle supplementary to AOB. a. EOD b. DOB c. AOE d. BOC 6. Find the area of a circle with diameter 31.6 cm, both in terms of π and to the nearest tenth. Use 3.14 for π. a. A = π cm cm 2 b. A = 63.2π cm cm 2 c. A = 31.6π cm cm 2 d. A = π cm cm 2 1

2 Name: 7. Use the diagram to find the measure of PML. a. m PML = 59 b. m PML = 21 c. m PML = 38 d. m PML = Which of the following is NOT a measure of an angle in the figure below? a. 27 b. 29 c. 54 d Find the circumference of the circle to the nearest tenth. Use 3.14 for π. a in. b in. c in. d in. 10. Riggoletto s Portraits specializes in making circular portraits of people. A large portrait is 78 in. in diameter. A medium portrait is 26 in. in diameter. Estimate the difference between the areas of the two sizes of portraits. Use 3.14 for π. Round your answer to the nearest whole number. a. about 82 in 2 b. about 4245 in 2 c. about in 2 d. about 163 in The diameter of Joe s car wheel is 18 inches. What is the circumference to the nearest inch? Use 3.14 for π. a. 39 inches b. 57 inches c. 113 inches d. 254 inches 12. A large concrete block is used for the cornerstone of a building. The block is 13 ft deep, 11 ft wide, and 16 ft long. What volume of concrete is needed to make this block? a. 189 ft 3 b. 159 ft 3 c. 40 ft 3 d ft The circumference of a circle is 32 centimeters. Which is closest to the radius? a centimeters b. 5.1 centimeters c. 16 centimeters d. 5.3 centimeters 2

3 Name: 14. Find the volume of the composite figure. a. 6,786 ft 3 b. 4,914 ft 3 c. 1,872 ft 3 d. 2,032 ft A circle with radius 16 centimeters is inscribed in a square. Which is the area of the shaded region? a square feet b square feet c square feet d square feet 16. The lengths of two sides of a triangle are 3 cm and 7 cm. What can you conclude about the maximum length of the third side of the triangle? a. The maximum length of the third side must equal 10 cm. b. The maximum length of the third side must be greater than 10 cm. c. The maximum length of the third side must be less than 10 cm. d. The maximum length of the third side must equal 4 cm. Determine whether it is possible to form a triangle using the set of segments with the given measurements. Explain your reasoning in., 8.7 in., 15.4 in m, 5 m, 18.9 m 19. Find the values of x and y. 20. Find the surface area of the prism shown without a top. 3

4 Name: 21. Identify the angles that have a greater measure than AHB. a. BHC b. CHD c. DHF d. FHG e. GHA 22. Maria has a ramp that she uses for racing model cars. Her cousin Sophia wants to build a ramp whose dimensions are three-fourths the size of Maria's ramp's. What will be the height of Sophia's ramp? 23. Solve for x. 24. Matilda builds a model as shown in the figure. The model is a right rectangular prism and a small cube. How much area does she have to paint if she paints all of the model s exterior? Explain. 25. A farmer drew the following figure as an outline for a barn that he is planning to build. Part A: How many square meters of lumber will he need to build the exterior of the barn including the roof and floor? Show your work. Part B: How many cubic meters of straw would it take to fill the barn all the way to the roof? Show your work. 4

5 Geometry Test Review Answer Section 1. ANS: D OBJ: Using Proportions to Find Unknown Scales STA: MACC.7.G ANS: B OBJ: Using Proportions to Find Unknown Scales STA: MACC.7.G ANS: D The vertical cross section is an isosceles triangle whose height is the same as the pyramid, 14 yards, and whose base is 12 yards. STA: MACC.7.G ANS: B STA: MACC.7.G ANS: B STA: MACC.7.G ANS: A OBJ: Finding the Area of a Circle STA: MACC.7.G ANS: C OBJ: Using Properties of Angles to Label Triangles STA: MACC.7.G ANS: A Since BFC, CFD, and DFE form a straight line, the sum of their measures is 180. An equation that relates the measures of the angles is m BFC + m CFD + m DFE = 180. Substitute ( 2x + 12) for m BFC, 2x for m CFD, and 60 for m DFE. Then solve for x. ( 2x + 12) + ( 2x) + 60 = 180 2x + 2x = 180 4x + 72 = 180 4x = x = 108 4x 4 = x = 27 Since no angle has a measure of x, 27 is not a measure of any angle in the figure. STA: MACC.7.G ANS: D OBJ: Finding the Circumference of a Circle STA: MACC.7.G ANS: B STA: MACC.7.G ANS: B STA: MACC.7.G ANS: D OBJ: Application STA: MACC.7.G ANS: B 14. ANS: A OBJ: Finding the Volume of a Composite Figure STA: MACC.7.G ANS: D 16. ANS: C 1

6 17. ANS: Yes. It is possible to form a triangle because = 15.7, and 15.7 is greater than ANS: No. It is not possible to form a triangle because = 17, and 17 is not greater than ANS: x = 54; y = 41 STA: MACC.7.G ANS: 32 square centimeters STA: MACC.7.G ANS: A, D A, D: Since BHC and FHG are vertical angles, their measures are the same. So, m BHC = 63. B, E: Since x = 63, substitute 63 for x in the expression ( x 5). ( 63 5) = 58 So, m CHD = 58. Since CHD and GHA are vertical angles, m GHA = 58. C: Since AHB, BHC, and CHD form a straight line, the sum of the measure of the angles is 180. Solve for m AHB. m AHB + m BHC + m CHD = 180 m AHB = 180 m AHB = 180 m AHB = 59 Since AHB and DHF are vertical angles, m DHF = 59. STA: MACC.7.G ANS: 48 inches STA: MACC.7.G ANS: x = 64 2

7 24. ANS: Matilda has to paint 1,470 square inches. Find the surface area of the cube. S C = 2 w + 2 h + 2wh = 2 ( 4) ( 4) + 2 ( 4) ( 4) + 2 ( 4) ( 4) = = 96 The surface area of the cube is 96 square inches. Find the surface area of the rectangular prism. S P = 2 w + 2 h + 2wh = 2 ( 17) ( 14) + 2 ( 17) ( 15) + 2 ( 14) ( 15) = = 1,406 The surface area of the rectangular prism is 1,406 square inches. Add the surface areas of the cube and the rectangular prism ,406 = 1,502 The parts of the surface area where the cube rests on the prism will not be painted. So, subtract 2 times the overlapping area. 1, = 1, = 1,470 Rubric 1 point for answer; 2 points for explanation STA: MACC.7.G.2.6 3

8 25. ANS: Part A: 2872 m 2 ( ) + ( ) + (18 22) + (2 1 2 = ) + ( ) = 2872 Part B: 10,296 m È 3 Ê ( ) Ë Á ÎÍ = (7920) + (2376) = 10,296 ˆ OBJ: Finding the Volume of a Pyramid Finding the Surface Area of a Prism STA: MACC.7.G.2.6 4