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Task 1: Knowledge and Understanding questions 1. 2. Perform the following conversions: a. 428 cm to hm (1 mark) b. 2748 yd to km (2 marks) 0. 7.0 m to ft (2 marks) a. Calculate the surface area of a rectangular prism which is 2 cm x 4 cm x 6 cm. (3 marks) b. Calculate the volume of this figure. (2 marks) . Calculate the height of a lean-to roof that has a slanted height of 325 cm and an angle of elevation of 22. Round your answer to the nearest cm. Include a diagram. (4 marks) . Calculate the length of a staircase that is 3.2 m high, and has a slanted height of 4.7 m. Round your answer to one decimal place. Include a diagram. (5 marks) . A lifeguard spots a swimmer in the lake at an angle of depression of 32. He spots a sailboat, further out, at an angle of depression of 13. If the lifeguard is 36.5 dm away from the swimmer and 84.7 dm away from the sailboat, how far is the swimmer from the sailboat? Round your answer to the nearest tenth of a dm. Include a diagram. (6 marks) Task 2: Thinking questions 6. a. Create the net for a soup can with the dimensions of your choice. Make sure to be realistic. Label the dimensions. (3 marks) b. Calculate the surface area of the can. (Hint: Area of a circle = Jrr2 (3 marks) c. Calculate the volume of the can. (Hint: Volume = area of the base X height ) (3 marks) 7. Create a question involving a real-world application that can be solved by the sine or cosine law. Draw a triangle that represents the situation and solve the triangle. (10 marks) 8. Draw a perspective drawing of an item that you would nd in your home. (6 marks) Task 3: Communication questions 9. Imagine you have decided to design an item of furniture for your home. a. Name the item you wish to make. (1 mark) b. Describe the size of the item. Why have you chosen this size? (2 marks) c. Describe the shape of this item. What geometric shapes will this item include? (2 marks) d. Describe the material you will use. What advantages do these materials have over others? What are some unacceptable materials for this item? (3 marks) e. Are there any standard requirements related to this item? Explain. (2 marks) f. Discuss some of the other constraints associated with this item. (2 marks) 10. A cardboard box is being designed to hold a volume of 729 cubic cm of salt. a. What dimensions will minimize the cost of producing the box? (3 marks) b. What dimensions would you recommend for the box? Why? Give three or four reasons for your answer. (4 marks) 11. Define the three elements that must be in balance when designing an object. Give an example, and explain how you would balance these three factors in your design. Which of these factors do you feel would be the most important in designing this item? (6 marks) 12. Here is the model of a three-dimensional structure. Based on this structure, you will make some hand-drawn sketches. Scan them or photograph them with a phone or digital camera, and place them into your Word doc. Three-dimensional structure: Direction of views Top 8. Create an orthographic diagram (composed of front, top, and side views) for this model. Each cube is exactly 1 inch in length, width, and height. Use a scale of 1:2. For your side view, use the right side. (4 marks) b. Create an isometric diagram for this model. Remember to use \"learnstyleslgthgngr' for your drawing. Use the same measurements and scale as in part a. Draw your diagram as if you were looking at the front right-hand corner. The diagram here has been drawn from the front left-hand corner. (4 marks) 13. The following diagram is the oor plan for a cottage. BEDROOM BEDROOM 12-o- x 1121' Main Floor a. Calculate the scale. (2 marks) b. Calculate the size of the kitchen to the end of the countertop. Assume the table is in the dining room. (4 marks) 14. An interior designer plans to use triangular tiles that are 8 cm x 9 cm x 13 cm for a backsplash. In order to fit them together properly, she needs to know the size of the angles on the tile. Calculate the three angles on the tile, accurate to one decimal place. Include a diagram. (11 marks)