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(@ (E (F ( )? )` )l *! *# *$ *( ** * * * + + -= -? -B -C -M . . . . . /o /q / / 0 1 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 5-5-<-- -X-A-4-`-\-@"_-D&+-)-@-7.-l0ek-H27-h5 UNIT 7: WORKING WITH SHAPES IN TWO DIMENSIONS EVEN QUESTIONS 2 - 40 Please refer to this information while working on problems in this packet. (Place SUMMARY information, page 32, here.) 2. A car tire stands about 23 inches tall. a. What is the diameter of this tire? b. How far will the tire move if the tire rolls one complete revolution? c. If you drive on this tire 10,000 miles during a year, about how many complete revolutions does the tire roll? (Hint: Convert the units so that they are all the same.) What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the anwers(s). Your answer(s) are (make sure you are close to your estimate and the units used are correct): 4. An athletic club has a small running track, shaped as shown below. Place track, page 37, here. a. Recognize that the ends can be placed together to form a circle. What is the diameter of this circle? What is the length of the straight sections? b. Compute the circumference of this circle. Add this distance to the length of the two straight sections to find the total distance around the track. c. How many laps would you need to complete to jog one mile? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the anwers(s). Your answer(s) are (make sure you are close to your estimate and the units used are correct): 6. A certain firm produces vegetables grown in greenhouses. They use ten rectangular-shaped greenhouses, each one measuring 30 x 200 inside. a. How many square feet does each greenhouse have under roof? b. If one acre is 43,560 square feet, how many acres are within all the  greenhouses? (Round to 2 decimal places.) What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the anwers(s). Your answer(s) are (make sure you are close to your estimate and the units used are correct): 8. Its time to fertilize your lawn with your new fertilizer spreader. The bag of fertilizer youve bought says it will cover 5000 square feet. Below is a sketch of your house lot, showing the house, driveway, and patio - areas that wont be fertilized. Place house lot, page 39, here. a. What is the total area of the lot? b. What is the area of your lot that wont be ferilized? c. Use the results of the above calculations to find the area of your lot to be fertilized. Do you have enough fertilizer to apply to your lot at the recommended rate? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the anwers(s). Your answer(s) are (make sure you are close to your estimate and the units used are correct): 10. The irregular field from Exercise 9 can be divided into recognizable figures to determine the total area of the field. Use the diagram below of an irregular field broken up into two triangles and a trapezoid to find the acreage of the field. Place field diagram, page 39, here. a. Identify the two triangles and trapezoid by the letters of their corners. b. Identify from the diagram the dimensions needed for the calculation of area for each of the three figures. c. Calculate the area for each figure, and the total area for the field. d. Since 43,560 square feet is one acre, convert the total area of the field to acres. 12. What must be the length of a label to fit around a can that is 3 in diameter, allowing for 1/4 overlap for pasting? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure you are close to your estimate and units used are correct): 14. A real estate agent must be able to answer questions about a houses floor plan. Use the measurements provided on the simplified floor plan below to determine the living area for the home. Place floor plan, page 41, here. a. What is the total area of the house, including living area and garage? (Hint: Divide the total floor area into pieces that you recognize, such as squares and rectangles, and add their areas together.) b. When reporting a homes living area, you do not normally include the garage area. What is the floor space of this home that is living area? 16. The floor of a convention center meeting room is being prepared for a gathering. You must estimate about how many chairs will be needed. The convention center floor measures 80 feet across at the front, and 120 feet across at the rear. The back row will be 150 feet from the front. Allow for three 4-foot-wide aisles running from front to rear (see diagram below). Place diagram, page 43, here. a. What is the total floor area? b. What is the area of the aisles? c. Subtract the area of the aisles from the total floor area to find the area available for seating. Allow a 2x 3 space for each seat. Approximately how many chairs can be placed in the seating area? d. What are some reasons why this calculation may be slightly incorrect? Do you think that the estimated seating capacity is a little high or a little low? 18. A retirement home provides a garden area for the members to exercise. A circular garden and walkway has a diameter of 25 feet. How far would one walk if they were to walk around this garden 5 times? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure you are close to your estimate and units used are correct): 20. You are going to retile your den floor. The floor in your den is 12 feet wide and 15 feet long. The 12 x 12 tiles youd like to use are on sale for $0.99 each. a. How many square feet of tile will it take to cover your den floor (ignore waste for this exercise)? b. How many square feet will each tile cover? c. What will be the estimated cost for tiles to cover your floor? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure you are close to your estimate and units used are correct): 22. You are planning to paint the inside walls of your master bedroom. The label on the paint can says that it will cover about 300 square feet for rough-textured wall. As a rough estimate, you can neglect the space for the windows and doors. The walls are eight feet high. Two walls are 12 feet wide, and two walls are 15 feet wide. The drawing below shows these dimensions. Place diagram, page 45, here. a. What shape can you use for the walls when calculating the area? b. What is the area of each of the walls? What is the total area? c. How many cans of paint should you need to paint the walls in this room? d. What effect would the windows and doors have on this estimate? 24. A certain 4 x 8 sheet of plywood weighs about 32 pounds. a. Identify the shape of the 4 x 8 sheet of plywood. Is it square, rectangular, or circular? b. What is the area of the sheet of plywood? c. What is the weight of each square foot of the plywood? d. If a section with an area of five square feet is removed from the sheet, what will the remaining plywood weigh? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure you are close to your estimate and units used are correct): 26. A computer display screen can show 80 characters on a row, and show up to 25 rows on the screen at one time. a. What is the maximum number of characters that can be displayed on the screen at one time? b. If each character requires 2 bytes of computer memory, how many bytes of memory must be allocated for one screen-full of display? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure you are close to your estimate and units used are correct): 28. A rooftop, as shown below, is to be re-roofed with asphalt and felt shingle material. Shingles are sold by the square. Each square covers 100 square feet. Place rooftop drawing, page 48, here. a. What is the shape of the roof surfaces? b. What is the area of the roof to be decked? c. How many squares of shingles are needed to cover this area? (Round up to nearest whole square.) 30. Tack strip is placed around the perimeter of a room (excluding the doorways) to secure carpet. Use the floor plan below to compute how much tack strip is needed to carpet the floor. Place drawing, page 49, here. a. What is the perimeter of the room and hallway shown? (Assume that all the corners are perpendicular.) b. If each 3-foot doorway is deducted from the total, how much tack strip is needed to carpet the rooms? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure you are close to your estimate and the units used are correct): 32. A pipe support clip is needed for a 2 pipe, as shown below. What length of strapping will be needed to make it? (Round to the nearest 0.1.) Place diagram, page 49, here. What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure you are close to your estimate and the units used are correct): 34. A rectangular duct is to be replaced with a round duct. The rectangular duct is 12 wide and 6 high. If you were to cut straight through this duct, the shape would represent a rectangle. The area of this figure is called the cross- sectional area as shown below. Place duct picture, page 50, here. a. What is the cross-sectional area of this rectangular duct? b. You have various round ducting with diameters of 4, 6, 8 and 10 available to you. What is the cross-sectional area of each of these ducts? c. Which ducting should you choose to most closely approximate the cross- sectional area of the existing ductw.ork? 36. You are insulating a replacement section of air-conditioning ductwork. The ductwork is round, with a diameter of 14. a. How many inches of insulation are needed to wrap around the duct? (Round to nearest inch.) b. If this section of ductwork is 65 feet long, how many square feet of insulation will be needed to cover the duct? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure you are close to your estimate and the units used are correct): 38. A round steel rod is able to bear a tensile force of 16,000 pounds for each square inch of cross section. A rod capable of bearking 125,000 pounds is needed. Rods with diameters of 2, 3, and 4 are being considered. Place rod drawing, page 51, here. a. What is the cross-sectional area of the 2 rod? the 3 rod? the 4 rod? b. What load will the 2-diameter rod bear? the 3-diameter rod? the 4 rod? c. Which is the smallest rod able to bear the load? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure you are close to your estimate and 7the units used are correct): 40. Two identical pulleys on a belt sander that you built are 24 inches apart, as shown below. Each pulley has a diameter of 4. Calculate the length of the sanding belt needed. Place sander drawing, page 52, here. What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure you are close to your estimate and the units used are correct): DSET|(H-0/- *6*/-DSET(HX-9>96*=9DSETR -\---   -LUnit 7 Even Questions