MATH 101 2021 GS 11.9.2 Project: Geometry Honors, Performance Task: The Subway Stop Project. All Worked Solutions.

MATH 101 2021 Honors Geometry Project 11.9.2. GS 11.9.2 Project: Performance Task: The Subway Stop Project Geometry Honors Points Possible:150 The Scenario: The city subway is being extended to include a new stop i ...

MATH 101 2021 Honors Geometry Project 11.9.2. GS 11.9.2 Project: Performance Task: The Subway Stop Project Geometry Honors Points Possible:150 The Scenario: The city subway is being extended to include a new stop in a large open plaza. The entrance to the new stop needs to be architecturally distinctive and energy efficient, but it also needs to fit within the budget. As part of your summer job with the Department of Transportation (DOT), you've been asked to review design ideas from three different firms and recommend which firm should be chosen to develop its idea into a full design proposal. The Project: Use the information provided in the Performance Task to learn more about the proposed designs, the requirements the structure must meet, and the estimated project costs before you recommend which architectural firm should fully develop its proposal. The questions below will help you gather information and prepare your recommendation. Remember to show your work. The Plaza (information when you click on Proposals) 1. What is the area of the entire plaza? (1 point) 2. What is the area of the plaza available for the subway entrance? (1 point) Amber Been a = 40,000 ft 23. Draw a picture showing how much of the total area available for the subway entrance you think should be covered by the new structure, and explain your reasons. (3 points: 1 point for drawing, 2 points for explanation) The Firms' Designs 4. Review the designs proposed by each of the three architectural firms. Complete the following table to summarize your understanding of each proposal. (21 points: 1 point for each cell in rows 1, 3, and 5; 2 points for each cell in rows 2 and 4.) Firm Sill, Linder, and Sons Designs with a Point Davidson Domes The structure cannot cover all of the area so pedestrians can BRANTLEY Wain around it . However , it needs to be large enough to be noticeable . Cylinder Pyramid Dome Mimics Shape Interest and compliments of fountain ,- symmetry to plaza dramas contrast shape of with fountain fountain clear glass Glass and Glass , reflection panels metal fabric unobstructed view through all variety of view , distinctive sides natural light ground lighting BT Tower Louvre Pyramid Reichstag BuildingThe Scenario: The city government requires that the diameter or longest edge of the new structure not exceed 70 feet. Some members of the DOT think the structure should maximize the total enclosed space, while others think it's more important to maximize the footprint, or floor space. Click each structure in the Requirements to see its dimensions. Use this information to determine which structure you think best meets the requirements and needs. Understanding the Calculations Required 5. What measurement, area, volume, or surface area, do you need to calculate in order to determine the floor space, or footprint, of each structure? (1 point) 6. What measurement do you need to calculate in order to determine the amount of space each structure encloses? (1 point) To determine the floor space we need to know the surface areas of each structure. To determine tie amount of space, we need to know the volume of each structure.7. List the two measurements (area, volume, or surface area) needed to estimate the amount of material required to cover each structure, not including the floor. Explain how these measurements would be used. (2 points: 1 point for the measurements, 1 point for the explanation) The Plaza 8. Which formula would you use to calculate the floor space of Firm 1's structure? Explain your choice. (Refer to the Formula table on page 3.) (2 points: 1 point for the formula, 1 point for the explanation) 9. Calculate the floor space of Firm 1's structure. (2 points) To estimate the amount of material , we need to know the surface area and area of tie base . To remove tie base from tie surface area, we'll need to subtract it from tie total surface area I'd use the area of a circle formula : Jer ? This formula will provide tte area of tree floor space or specifically , tie base of tree cylinder . 3848.45ft 210. Which formula would you use to calculate the total enclosed space of Firm 1's structure? Explain your choice. (Refer to the Formula table on page 3.) (2 points: 1 point for the formula, 1 point for the explanation) 11. What is the total enclosed space of Firm 1's structure? Show your calculations. (2 points) 12. Write a formula to estimate the amount of material required to cover Firm 1's structure, not including the floor. Explain your reasoning. (2 points: 1 point for the formula, 1 point for the explanation) 13. Use the formula from question 12 to estimate the amount of material required to cover Firm 1's structure, not including the floor. Show your calculations. (2 points) I'd use tie formula for tie volume of a cylinder ; Iran : Volare shows how much enclosed space is in of material m=(2ar2 +2 # rn) - Jcr 2 theTObase find the surface area excluding , we need to sub-7rad toe area of 1-te base from the entire surface area . This means we'll use +2 surface area of a cylinder formula and the area of a circle m= 18,043 . 14 ft 2How Does Firm 2 Measure Up? 14. Which formula would you use to calculate the floor space of Firm 2's structure? Explain your choice. (Refer to the Formula table on page 3.) (2 points: 1 point for the formula, 1 point for the explanation) 15. What is the floor space of Firm 2's structure? Show your calculations. (2 points) 16. Which formula would you use to calculate the total enclosed space of Firm 2's structure? Explain your choice. (Refer to the Formula table on page 3.) (2 points: 1 point for the formula, 1 point for the explanation) I would use the area of a square formula; b? Tie Floor space (the base) is a square , so to find the space it tares up, I need to know trearea . I would use the volume of a pyramid formula : 13 ban . Volume represents teetotal enclosed space and tie structure is a pyramid .17. What is the total enclosed space of Firm 2's structure? Show your calculations. (2 points) 18. Write a formula to estimate the amount of material required to cover Firm 2's structure, not including the floor. Explain your reasoning. (2 points: 1 for the formula, 1 for the explanation) 19. Use the formula from question 18 to estimate the amount of material required to cover Firm 2's structure, not including the floor. Show your calculations. (2 points) How Does Firm 3 Measure Up? 20. Which formula would you use to calculate the floor space of Firm 3's structure? Explain your choice. (Refer to the Formula table on page 3.) (2 points: 1 point for the formula, 1 point for the explanation) m=2bs + b 2- b. 2 To find the surface area excluding toe floor , free base area can be subtracted from me 2bs the total surface area of a pyramid formula. This can be simplified to abs . m= 2bs m= 2.68 . 53.26 ME 7243.36ft 2 The base of a geodesic dome is a circle because the sphere is eat in half . Tie Formula for area of a circle is Jer ?21. What is the floor space of Firm 3's structure? Show your calculations. (2 points) 22. Which formula would you use to calculate the total enclosed space of Firm 3's structure? Explain your choice. (Refer to the Formula table on page 3.) (2 points: 1 point for the formula, 1 point for the explanation) 23. What is the total enclosed space of Firm 3's structure? Show your calculations. (2 points) 24. Write a formula to estimate the amount of material required to cover Firm 3's structure, not including the floor. Explain your reasoning. (2 points: 1 for the formula, 1 for the explanation) 25. Use the formula from question 24 to estimate the amount of material required to cover Firm 3's structure, not including the floor. Show your calculations. (2 points) You would use the formula for volume Of a sphere ,:* . 4-3 Irs and divide it by 2 because a done is only half of a sphere, so you 're actually finding the volume of a hemisphere. . we need to subtract the basearea m=(4T¥) - Tera from tree total surface area. Because it is a tensprog we need to divide toe surface area formula by 2 . MI 3,421.2 ft 2Meeting the Requirements 26. Use your calculations from the previous questions to complete the following table and compare the three structures. Round each answer to the nearest whole number. (3 points: 1 point for each row) Firm Floor space (ft2) Enclosed space (ft3) Surface area (ft2) (exclude floor) 1: Cylinder 2: Pyramid 3: Dome 27. Some members of the DOT want to maximize floor space. Which structure has the largest footprint? (1 point) 28. Other DOT members think the structure should enclose the largest amount of space possible. Which structure would they prefer? (1 point) The pyramid has the largest footprint . They would prefer tie cylinder .29. Having a large enclosed space has advantages, but it can be more expensive to heat and cool. Assume an air conditioner uses about 4 BTUs/cubic foot each hour (a BTU is a measure of energy). How many BTUs will the air conditioner need to produce each hour to cool the structures? Hint: Multiply the enclosed space by the number of BTUs needed per cubic foot. (3 points) 1: Cylinder 2: Pyramid 3: Dome 30. The cost of the building materials will depend in part on the surface area of the structure. The larger the surface area to be covered, the more it will cost to build. Which structure has the smallest surface area? (1 point) 31. Which firm's design would you recommend? Why? As long as the design meets the requirements, there is no right or wrong answer. (3 points) The dome has the smallest surface area . I would recommend firm 2'S design .It meets the requirement of edges shorter than 70 Et and will be te cheapest to cool and treat. It also should be structurally strong and able to withstand damage .Project Costs The budget for the initial phase of construction must be $450,000 or less. The overall cost will be determined by the materials used. Compare the cost of building your structure using different options for materials. Start by using only the highestcost options. Will you be able to use these materials and stay within the budget? Next, identify a different mix of materials to put in your recommendation. Complete each table following these guidelines: (find these in “Project Costs”) • Select a surface material to cover the structure. • Use cables, structural rods, or struts that are all made of the same material. • For structures that use connectors, you need three different types of the same material. The total price of the connectors is the sum of three different types. • Round the values in the Cost column to the nearest dollar. 32. High Cost Options. Identify the highest-cost material for each component and calculate the associated cost. 13 points: 1 point for each table cell Material(s) Amount Price Cost Surface Cables, Structural eachTotal Cost Main Components 33. Can you build your structure using only the most expensive materials and stay in budget? Why or why not? (1 point) Choosing Materials and Calculating Costs 34. Your proposed materials. Select a material for each component that you think should be used and calculate the associated cost. Make sure that the total cost of using your proposed materials is within budget. (13 points: 1 point for each table cell) Material(s) Amount Price Cost Surface Cables, Structural Rods, or Struts Connectors Total Cost each $420,37035. Draw a picture of the structure you are envisioning. Label the following: 1. The dimensions 2. The surface materials (4 points: 2 points for drawing, 2 points for labels) Contract Now it's time to make a recommendation. Prepare a brief report that outlines your recommendation for the idea that will be developed into a full design proposal. Make sure you demonstrate that the structure meets the city requirements, addresses the DOT concerns, and stays within budget. 36. Complete the report below so your manager knows the recommendation you're making and understands your thinking. Be sure to do all of the following: • Select the recommended firm. (1 point) • Describe the shape of the structure the firm should further develop. (2 points) • Describe the dimensions of the structure. (2 points) • List the materials to be used for the structure. (3 points) • Identify the total cost of this structure. (1 point) • Explain your reasons for recommending this structure. Make sure to include how it meets the DOT requirements and budget. (2 points) Reason for recommendation The structure is in tie shape of a pyramid , which adds interest and contrast The shape contrasts the plaza's fountain and serves as as a focal point of tte plaza. The structurehas a base of 68 ft and a height of 41 ft, meaning it will easily fit within tie set parameters . The use of colored glass makes the pyramid stand out.We'll also use high-quality materials line bronze And stainless steel . The overall cost will be $420,370 , which leaves about $30,000 to treating /cooling te building and flooring. Thebuilding is underbudget and fits DOT requirements of edges less than 70ft.The Ticket Office The city wants Davidson Domes to design a new ticket office for the subway. The outer shell of the office will be a dome with a diameter of 60 feet and a height of 30 feet. You have been asked to help with the plans. 37. The cross-section of the dome is a semicircle whose radius is 30 feet. Make a sketch showing the cross-section of the dome. (4 points) 38. You want to sketch the cross-section of the dome on a coordinate grid. You're going to locate its center at (0, 0). Write an equation for a circle whose diameter is 60 feet and center is (0, 0). (4 points) 39. Rewrite your equation from question 38 to isolate y2. (In other words, solve for y2.) Then solve for y by taking the principal square root of both sides. (4 points: 2 points for isolating y2 and 2 points for the final equation) + (y - O)2=302 1×-012+4*-012=302 Use the equation from question 39 to complete the table of values. When necessary, round yvalues to the nearest tenth. Then graph the result to show a cross-section of the ticket office. (8 80In the center of the dome, there will be a large cylindrical ticket kiosk that is 24 feet tall. The top of the kiosk just touches the dome. Assume that the entrance to the dome is at (30, 0). 41. Use your graph to find how far the edge of the kiosk is from the entrance, to the nearest foot. Explain how you found your answer. (Hint: Find the x-value of the point where y = 24 that is closest to the entrance.) (8 points) 42. When you take the square root of both sides of an equation, you use the symbol ± to show that a square root can be positive or negative. Why were you able to leave out the negative possibility when solving for y in question 39? (2 points) Copyright © 2018 Apex Learning Inc. Use of this material is subject to Apex Learning's Terms of Use. Any unauthorized copying, reuse, or redistribution is prohibited. Apex Learning ® and the Apex Learning Logo are registered trademarks of Apex Learning Inc. 4=30-24 (6/24) FÉÉ "• (9O0-36)t(O-S76)- 864576T Tagg =16.97units@ With tie picture we can see that tie edge of the kiosk will have a positive y - valve.