Name: Period Score /27 Version: B

Transcription

1 Name: Period Score /27 Version: B Transformations, Similarity & Surface Area Completion Complete each statement. 1. A set of values that compares quantities measured in the same units is called a(n) 2. Similar triangles have different sizes, but equal 3. A relationship that shows two ratios are equal is called 4. An increase in the dimensions of an object by a constant factor is called a(n) 5. A two-dimensional closed figure made of three or more line segments is called a(n) 6. A figure that has all sides and all angles equal is a(n) 7. A decrease in the dimensions of an object by a constant factor is called a(n) 8. Figures that have equal angles and proportional sides are Multiple Choice Identify the choice that best completes the statement or answers the question. 9. What is the angle of rotation in the figure? a. 15 b. 20 c. 30 d. 60 1

2 10. Identify any symmetry shown in the flag of Canada. a. no symmetry c. rotation symmetry b. more than one kind of symmetry d. vertical line symmetry 11. Each of the 9 identical cubes in the object has dimensions of 3 cm. What is the exposed surface area of the object, excluding the base? a. 261 cm 2 b. 279 cm 2 c. 243 cm 2 d. 288 cm A scale of 6:8 means a. there are 6 units of the image for every 8 units of actual size b. there are 8 units of the image for every unit of actual size c. there are 8 units of the image for every 6 units of actual size d. there are 6 units of the image for every unit of actual size 2

3 13. In the figure shown below, the hole in the figure extends straight through the to the other side. Calculate the total surface area of the figure. a cm 2 b cm 2 c cm 2 d cm Garth makes a doughnut with a flat top and a flat bottom. He plans to cover all surfaces of the doughnut with a sugar glaze. What is the surface area Garth must cover? Use the π key on your calculator rather than a cm 2 b cm 2 c cm 2 d cm 2 3

4 15. Calculate the surface area of the block. a. 850 cm 2 b. 886 cm 2 c. 862 cm 2 d. 869 cm Advertising posters often show smaller images of large objects (like a car) or larger images of small objects (like a calculator). If an actual object has a length of 38 cm and the image on the poster is 133 cm what is the scale used to make the poster? a. 8 : 3 c. 2 : 7 b. 3 : 8 d. 7 : The scale diagram below shows a cross-section of a pipe. The scale used to create the diagram is 1:6. What is the inside diameter of the actual pipe? a. 48 cm b. 7 cm c. 4 cm d. 42 cm 18. Triangle B is drawn from Triangle A using a scale of 1:5. If the hypotenuse of Triangle A is 10 mm, what is the length of the hypotenuse of Triangle B? a. 2 mm c mm b. 50 mm d. 2.4 mm 4

5 19. Joshua has drawn a scale diagram of a field using a scale of 3 mm : 1 m. How long should Joshua draw the line from A to C if the actual distance is 14 m? a. 42 mm c. 126 mm b mm d. 14 mm Short Answer Show any work and the answer in the space provided. 20. In a drafting class, students must create reductions of actual objects for technical diagrams. Emma wants to use a scale factor of 0.2 to draw a machine part. If the actual object has a width of 50 cm, what should the width of her drawing be? 21. Evan uses a map to determine the distance between his hometown and the closest campground. On the map, this distance is 2.6 cm. The actual distance is 18.2 km. What is the scale used on the map? 22. PAZ VCR. If PA = 18 cm, PZ = 15 cm and AZ = 31 cm, find the length of side VR if VC = 91.8 cm. 23. The screen on a digital camera is 2.7 cm wide. After a picture is taken, the image is 2.3% the size of the actual object. If the image of an object is as wide as the screen, what is the actual width of the object? 5

6 24. Determine the sum of both perimeters. 25. The length of side x is. 6

7 26. Draw the reflection image if the figure is reflected over the x-axis. 7

8 27. In the drawings shown, the scale factor used to create Figure B from Figure A is 8

9 Transformations, Similarity & Surface Area Answer Section COMPLETION 1. ratio 2. angles 3. proportion 4. enlargement 5. polygon 6. regular polygon 7. reduction 8. similar MULTIPLE CHOICE 9. D 10. D 11. A There are 29 faces exposed, 9 on the front, 9 on the back, 6 on the sides, and 5 on the top. Each surface is 9 cm 2. The total surface area exposed is 29 9 = 261 cm 2. The total exposed surface area is 261 cm A 13. D Surface area without the hole: 2 π π = cm 2 Surface area lost for holes in each end: 2π = cm 2 Surface area inside the hole: 2 π = cm 2 Total surface area: = cm A The SA of the dounght is outside edge + inside edge + 2Ê Ë Átop area area of the holeˆ 2πRh + 2πrh + 2 Ê πr 2 πr 2 ˆ Ë Á 2π π Ê π 6 2 π ˆ Ë Á = cm C 16. D 17. D 18. A 19. A 1

10 SHORT ANSWER cm 0.2 = 10 cm The width of her drawing should be 10 cm = 7 The scale used on the map is 1 : = 15 = 76.5 cm VR 23. Scale factor = size of image size of object 2.3% = 2.7 x = 2.7 x x = cm