1. CJ Developments Jin Ho Lee Jeong Eun Park Cara Leong Dang Wan Kim Caroline Poot

2. Our Process Research Consolidation Answers

3. How many people in a family? 2.61 children born/woman (CIA World Factbook) Round 2.61 children to 3 children Add 2 parents Equals 5 people in a family! However, our group mostly has 4 people in each family, so: 4 ± 1 people in a family!

5. Starting Questions How much water does each person use? What do we use water for? What is the best shape to store water in?

6. Answering Questions What do we use water for? Drinking Bathing Washing (dishes, laundry) Toilets Cooking

7. Answering Questions How much water does an average person use? Internet research 69.3 gallons per person for indoor purposes () laundry, shower, toilets, cooking, drinking Convert into litres 1 gallon = 3.78541178 litres  69.3 gallons ≈ 263 litres Leeway: 263 ± 2 litres

8. Answering Questions What is the best shape to store water in? Perimeter and Circumference vs. Area (of 2-D objects) Circle vs. Square Real life examples A cylinder is the best shape to store water in

9. How to calculate Surface Area Surface area of a cylinder is calculated by: Closed  (2πrh) + (2πr 2 ) = 2πr(r+h) Open  2πrh + πr 2 When r = radius of the cylinder’s base circle h = the height of the cylinder r h

10. How to calculate volume The volume of a cylinder that has a radius of r: π × r 2 × h Since a cylinder is a prism, the volume = base area × height r h

11. Calculation Total amount of water needed for entire village: 263 ± 2 L × 4 ± 1 people × 50 families × 14 days = 736 400 ± 26% L = 736 400 ± 200 000 L Volume of storage tank: 736 400 ± 200 000 L of water = 736.4 ± 200 m 3 This way, both the different sizes of family and different consumption of water are accounted for Maximum  756.4m 3 (around 757m 3 ) Minimum  716.4m 3 (around 717m 3 )

12. Best Choice (Max. Volume) Radius (m)Base Area (m 2 )Height (m)SA of Height (m 2 ) Cost of Metal ($) Concrete (m 3 )Concrete Cost ($)Total Cost ($) 13.14240.961514.0021283.961.41904.7822189 212.5760.24757.0010949.863.932513.2713463 328.2726.77504.677857.017.704926.0212783 450.2715.06378.506706.4312.728143.0114849 578.549.64302.806438.3119.0112164.2518603 6113.106.69252.336699.3926.5516989.7323689 7153.944.92216.297338.2735.3422619.4729958 8201.063.77189.258279.2345.4029053.4537333 9254.472.97168.229480.2456.7136291.6845772 10314.162.41151.4010916.0669.2744334.1655250

13. Radius vs. Height vs. Total Cost Radius (m)Height (m)Total Cost ($) 1 240.9621964 2 60.2413077 3 26.7712236 4 15.0614142 5 9.6417734 6 6.6922660 7 4.9228767 8 3.7735982 9 2.9744260 10 2.4153577

14. Best Choice (Min. Volume) Radius (m)Base Area (m 2 )Height (m)SA of Height (m 2 )Cost of Metal ($)Concrete (m 3 )Concrete Cost ($)Total Cost ($) 13.14228.231434.0020163.961.41904.7821069 212.5757.06717.0010389.863.932513.2712903 328.2725.36478.007483.687.704926.0212410 450.2714.26358.506426.4312.728143.0114569 578.549.13286.806214.3119.0112164.2518379 6113.106.34239.006512.7326.5516989.7323502 7153.944.66204.867178.2735.3422619.4729798 8201.063.57179.258139.2345.4029053.4537193 9254.472.82159.339355.8056.7136291.6845647 10314.162.28143.4010804.0669.2744334.1655138

15. Radius vs. Height vs. Total Cost Maximum VolumeMinimum Volume Radius (m)Height (m)Cost ($)Height (m)Cost ($) 1 241 22189 228 21069 2 60 13463 57 12903 3 27 12783 25 12410 4 15 14849 14 14569 5 10 18603 9 18379 6 7 23689 6 23502 7 5 29958 5 29798 8 4 37333 4 37193 9 3 45772 3 45647 10 2 55250 2 55138

16. Justification Viability vs. Cost Is it really that good to have a 26± 1m structure? Is it possible to have a 26 ±1m structure that will hold its weight? Amount of water used: Leeway for water use of people in case they need more water Level of Accuracy (nearest whole number): Easier to see the difference between figures

17. Justification For the cheapest cost, the height of the cylinder will be at least 25m, which is too high Water pressure For stability, if the radius is 1m larger, the height goes down by almost 10m Stability, pressure distribution

18. Our Storage Tank Has a capacity of 7437 000 ± 200 000L Is in the shape of a cylinder Dimensions: Radius: 4 metres Height: 14.5 ± 0.5 metres Cost: $14700 ± 150

19. How did we get our numbers? Base area: π × r 2 Height: Volume needed (m 3 ) ÷ base area Total surface area: 2πr(r+h) Cost of metal: $ (14 × total surface area) Volume of concrete: (radius + 0.5m) 2 × 0.2m Cost of concrete: $ (640 × volume of concrete) Total cost: $ (Cost of metal + cost of concrete)

21. Starting Questions What kind of grain are we storing? How much grain are we putting in storage? What kind of shape is the best for storing the grain?

22. Answering Questions What kind of grain are we storing? Grain can be used to make many types of food Rice, corn, oats, rye Bread for our purposes, we’ll pretend that we’re storing rice

23. Answering Questions How much grain are we putting in storage? The space that the cooked rice takes up is 3-4 times the space that uncooked rice takes up Each person eats about 300cm 3 of cooked rice per meal 300cm 3 of cooked rice ≈ 100cm 2 of uncooked rice

24. Answering Questions What kind of shape is best for storing the grain? Real life examples Cylinder has the largest area for a fixed perimeter Cylinders are also used for silos

25. Examples of Grain Storage http://www.dengie- crops.com/media/silos%20and%2 0lorry.JPG http://www.mawaterquality.org/gall ery/photos/hog%20grain%20storag e.jpg

26. Calculation 100cm 3 uncooked rice × 3 meals × 4 people × 50 families × 14 days = 840 000 cm 3 of uncooked rice 840 000cm 3 = 0.84m 3 Shed has to have a volume of 0.84m 3 round to 1m 3

27. Best Choice for Grain Storage RadiusBase AreaHeight Circumfere nce SA of Height TSA Cost of Metal Concrete Concrete Cost Total Cost 0.10.0331.80.620.0 280.40.164.3345 0.20.18.01.310.010.1141.80.2100.5242 0.3 3.51.96.76.997.30.2144.8242 0.40.52.02.55.05.577.00.3197.0274 0.50.81.33.14.04.867.00.4257.4324 0.61.10.93.83.34.562.50.5325.7388 0.71.50.64.42.94.461.60.6402.1464 0.82.00.55.02.54.563.10.8486.6550 0.92.50.45.72.24.866.70.9579.1646 1.03.10.36.32.05.172.01.1679.6752

28. Justification With radius of 0.2 the height have to be 8 to hold 0.84m 3. To have a structure with stability have to be radius of 0.3 and height of 3.5.

29. Justification Having a same cost stability will be better. So having lower height with longer radius is safer to hold the weight. It has plenty of space to put in a lot of grain

30. Our Grain Silo Is cylindrical Has a capacity of 1m 3 Dimensions: Cost: Of metal sheet: $100 ± 10 ($97.30) Of concrete: $150 ± 10 ($144.80) Total cost: $250 ± 20 ($242.10)

31. Work cited Where we got the amount of food and water per person : http://www.newsobserver.com/weather/drought/story/1016009.html. 1 Dec. 2008. : https://www.cia.gov/library/publications/the-world-factbook/. 1 Dec. 2008. Where we got the image of grain storage : http://www.dengie-crops.com/media/silos%20and%20lorry.JPG. 1 Dec. 2008. : http://www.mawaterquality.org/gallery/photos/hog%20grain%20storage.jpg. 1 Dec. 2008.