1. KFCs proposal By: Yu Rim Hyung Rae Seong Min Chloe Chloe Yuan ke Yuan ke

2. Introduction For the past few weeks KFC had being aiming to design, and price, a water and grain storage facility for a village that has fifty families. For the past few weeks KFC had being aiming to design, and price, a water and grain storage facility for a village that has fifty families. The storage facility must be able to contain a two week supply of water and grain. The storage facility must be able to contain a two week supply of water and grain. The walls and roof of the facility will be made out of metal sheet that costs $14 per m2. The walls and roof of the facility will be made out of metal sheet that costs $14 per m2. The facility must be placed on a 20cm thick concrete floor. The concrete costs $640 per m3. The facility must be placed on a 20cm thick concrete floor. The concrete costs $640 per m3. We must make every effort to keep the cost as low as possible. We must make every effort to keep the cost as low as possible.

3. How many peoples in a family? Research had shown that the average population of a family is around 4 ± 1(two adults and two children) Research had shown that the average population of a family is around 4 ± 1(two adults and two children) Therefore 50x4 ±1=200±50 people are included in this 50 families Therefore 50x4 ±1=200±50 people are included in this 50 families

5. http://www.globalspec.com/NpaPics/ 98/151694_081120042854_ExhibitP ic.jpg http://www.fruitland.org/vertical/Site s/%

6. What we found out in our research? In real life: water are stored in cylinders In real life: water are stored in cylinders Each person needs about 117Liters Each person needs about 117Liters 50 Families would need water of 245700 Liters 50 Families would need water of 245700 Liters Activities Activities Toilet Flush(40 Liters) Toilet Flush(40 Liters) Shower(34 Liters) Shower(34 Liters) Washing Clothes(26 Liters) Washing Clothes(26 Liters) Washing Dishes(14 Liters) Washing Dishes(14 Liters) Cooking(1 Liter) Cooking(1 Liter) Drinking (2 Liters) Drinking (2 Liters) Total117 Liters Total117 Liters

7. What is it the best solution? Cylinder Cylinder Stable Stable Circle gives the biggest area, but a sphere wouldnt be as stable, therefore we chose cylinder prism with circle on the bottom Circle gives the biggest area, but a sphere wouldnt be as stable, therefore we chose cylinder prism with circle on the bottom Cylinder with Radius of 2.35meters and height of 14.2 meters, with cost of $6685.6 to build Cylinder with Radius of 2.35meters and height of 14.2 meters, with cost of $6685.6 to build

8. Why is it the best solution? 50 families would need 245700 liters for living. 50 families would need 245700 liters for living. 1 Liter is converted to 1m 3 1 Liter is converted to 1m 3 245700 Liters = 245.7m 3 245700 Liters = 245.7m 3 During research, found that larger height makes the shape to be cheaper. Because the concrete base is the most expensive part of the whole building, so we are trying to keep the bottom area as small as possible During research, found that larger height makes the shape to be cheaper. Because the concrete base is the most expensive part of the whole building, so we are trying to keep the bottom area as small as possible However, base cannot be too small and just tall, because then it will collapse very easily. However, base cannot be too small and just tall, because then it will collapse very easily.

9. How we found the solution (justification)? Deciding on which dimension is the best. (Longest height) Deciding on which dimension is the best. (Longest height) To prevent the building from falling sideways, the diameter of the base has to be 3~4 times smaller than height maximum. To prevent the building from falling sideways, the diameter of the base has to be 3~4 times smaller than height maximum.

10. Volume of cylinder = Radius 2 x π x height Volume of cylinder = Radius 2 x π x height Maximum Height = 3 x Diameter Maximum Height = 3 x Diameter Therefore, Therefore, R 2 x 2R(Diameter) x 3 x π = 245.7 R 2 x 2R(Diameter) x 3 x π = 245.7 R 2 x 6R = 78.21 R 2 x 6R = 78.21 R 2 x R = 13.03 R 2 x R = 13.03 R 3 = 13.03 R 3 = 13.03 R = 2.35 R = 2.35

11. Using the Radius, find the height. R = 2.35 π = 245.7 2.35 2 x H x π = 245.7 H = about 14.2. H = about 14.2. Calculating the Total Surface area of the cylinder. Calculating the Total Surface area of the cylinder. (2.35 2 xπx 2) + (2.35x2xπx14.2) = 227.02 (2.35 2 xπx 2) + (2.35x2xπx14.2) = 227.02 227.02 x 14 = Cost of the Metal Sheet 227.02 x 14 = Cost of the Metal Sheet Metal sheet cost = $3421.6 Metal sheet cost = $3421.6 Calculating the Concrete volume. Calculating the Concrete volume. Concrete would have 0.5 meters added to the original container. the concretes radius = 2.85 height = 0.2 Concrete would have 0.5 meters added to the original container. the concretes radius = 2.85 height = 0.2 Volume of concrete = 2.85 2 x π x 0.2 = 5.1 Volume of concrete = 2.85 2 x π x 0.2 = 5.1 Cost of concrete = 5.1 x 640 = $3264 Cost of concrete = 5.1 x 640 = $3264 THE TOTAL COST = $3421.6+$3264 = $6685.6 THE TOTAL COST = $3421.6+$3264 = $6685.6

13. http://images.google.com/images?g bv=2&&hl=en&newwindow=1&q=ric e+storage&&sa=N&start=54&ndsp= 18 http://www.dengie- crops.com/media/silos%20and%20lorr y.JPG

14. What we found out in our research? One adult eats.25kg of rice per meal One adult eats.25kg of rice per meal If there are 4 people in the family, even though the children wouldnt eat as much as adults, but we will just make it 1kg for a family, in case extras members, and food supply. If there are 4 people in the family, even though the children wouldnt eat as much as adults, but we will just make it 1kg for a family, in case extras members, and food supply. 1x50x14=700kg 1x50x14=700kg

15. What is it the best solution? Radius: 0.3m Radius: 0.3m Base area: 0.3m^2 (3.14x0.3^2) Base area: 0.3m^2 (3.14x0.3^2) Height: 3.5m Height: 3.5m Circumference: 1.9m (3.14x0.3x2) Circumference: 1.9m (3.14x0.3x2) SA of the height: 6.7m^2 ( SA of the height: 6.7m^2 ( TSA: 6.9m^2 TSA: 6.9m^2 Cost of metal: $97.3 Cost of metal: $97.3 Concrete:0.2m Concrete:0.2m Concrete cost: $144.8 Concrete cost: $144.8 Total cost: $242 Total cost: $242

16. Why is it the best solution? Cylinder because it has the largest area with a fixed perimeter. Cylinder because it has the largest area with a fixed perimeter. Takes up all the rice we need without wasting a lot of volumes and money. Takes up all the rice we need without wasting a lot of volumes and money.

17. How we found the solution (justification)? Cylinder Cylinder 700kg goes into 700000cm^3 700kg goes into 700000cm^3 Which = 0.7m^3 Which = 0.7m^3 radius^2 x pi x height = 0.7 radius^2 x pi x height = 0.7 height is diameter x 3 height is diameter x 3 diameter is 2xradius diameter is 2xradius Therefore height= radius x 2 x 3 Therefore height= radius x 2 x 3 radius^2 x radius x 2 x 3 x pi=0.7 radius^2 x radius x 2 x 3 x pi=0.7 Radius^2x radiusx2x3=0.7/pi0.22 Radius^2x radiusx2x3=0.7/pi0.22 Radius^2x Radius =0.22/6 0.037 Radius^2x Radius =0.22/6 0.037 radius^3=0.037 radius^3=0.037 Radius=0.3 Radius=0.3

18. Citation Mathematics: water and grain storage facility project. 30 Nov. 2008. Mathematics: water and grain storage facility project. 30 Nov. 2008. Mathematics: water and grain storage facility. 30 Nov. 2008. Mathematics: water and grain storage facility. 30 Nov. 2008. Mathematics: water and grain storage facility project. 30 Nov. 2008. Mathematics: water and grain storage facility project. 30 Nov. 2008. Seong Min's personal interview with his math tutor. 30 Nov. 2008. Seong Min's personal interview with his math tutor. 30 Nov. 2008. Mathematics: water and grain storage facility project. 30 Nov. 2008. Mathematics: water and grain storage facility project. 30 Nov. 2008. Mathematics: water and grain storage facilty project. 30 Nov. 2008. Mathematics: water and grain storage facilty project. 30 Nov. 2008.