KFC’s proposalKFC’s proposal

By:By: Yu Rim Yu RimHyung RaeHyung RaeSeong Min Seong Min ChloeChloe

Yuan keYuan ke

IntroductionIntroduction For the past few weeks KFC had being For the past few weeks KFC had being

aiming to design, and price, a water and aiming to design, and price, a water and grain storage facility for a village that has grain storage facility for a village that has fifty families.fifty families.

The storage facility must be able to contain The storage facility must be able to contain a two week supply of water and grain.a two week supply of water and grain.

The walls and roof of the facility will be The walls and roof of the facility will be made out of metal sheet that costs $14 per made out of metal sheet that costs $14 per m2. m2.

The facility must be placed on a 20cm thick The facility must be placed on a 20cm thick concrete floor. The concrete costs $640 per concrete floor. The concrete costs $640 per m3.m3.

We must make every effort to keep the cost We must make every effort to keep the cost as low as possible. as low as possible.

How many people’s in a How many people’s in a family?family?

Research had shown that the Research had shown that the average population of a family is average population of a family is around 4 around 4 ±± 1(two adults and two 1(two adults and two children)children)

Therefore 50x4 Therefore 50x4 ±1=200±50 ±1=200±50 people are included in this 50 people are included in this 50 familiesfamilies

http://www.globalspec.com/NpaPics/98/151694_081120042854_ExhibitPic.jpg

http://www.fruitland.org/vertical/Sites/%

What we found outWhat we found out in our research?in our research?

In real life: water are stored in cylindersIn real life: water are stored in cylinders Each person needs about Each person needs about 117117LitersLiters 50 Families would need water of 50 Families would need water of 245700 245700

LitersLiters ActivitiesActivities

Toilet FlushToilet Flush (40 Liters)(40 Liters) ShowerShower (34 Liters)(34 Liters) Washing ClothesWashing Clothes (26 Liters)(26 Liters) Washing DishesWashing Dishes (14 Liters)(14 Liters) CookingCooking (1 Liter)(1 Liter) Drinking Drinking (2 Liters)(2 Liters)

TotalTotal 117 117 LitersLiters

What is it the best solution?What is it the best solution? CylinderCylinder

StableStable Circle gives the biggeCircle gives the bigge

st area, but a sphere st area, but a sphere wouldn’t be as stable, wouldn’t be as stable, therefore we chose cytherefore we chose cylinder prism with circle linder prism with circle on the bottomon the bottom

Cylinder with Radius Cylinder with Radius of of 2.35meters2.35meters and and height of height of 14.2 14.2 metersmeters, with cost of , with cost of $6685.6 $6685.6 to buildto build

Why is it the best solution?Why is it the best solution? 50 families would need 245700 liters 50 families would need 245700 liters

for living.for living. 1 Liter is converted to 1m1 Liter is converted to 1m33

245700 Liters = 245.7m245700 Liters = 245.7m33

During research, found that larger During research, found that larger height makes the shape to be height makes the shape to be cheaper.cheaper. Because the concrete base Because the concrete base is the most expensive part of the whis the most expensive part of the whole building, so we are trying to keep ole building, so we are trying to keep the bottom area as small as possiblethe bottom area as small as possible

However, base cannot be too small However, base cannot be too small and just tall, because then it will and just tall, because then it will collapse very easily.collapse very easily.

How we found the solution How we found the solution (justification)?(justification)?

Deciding on which dimension is Deciding on which dimension is the best. (Longest height)the best. (Longest height)

To prevent the building from To prevent the building from falling sideways, the diameter of falling sideways, the diameter of the base has to be 3~4 times the base has to be 3~4 times smaller than height maximum.smaller than height maximum.

Volume of cylinder = RadiusVolume of cylinder = Radius22 x π x height x π x height

Maximum Height = 3 x DiameterMaximum Height = 3 x Diameter Therefore,Therefore, RR22 x 2R(Diameter) x 3 x π = 245.7 x 2R(Diameter) x 3 x π = 245.7

RR22 x 6R = 78.21 x 6R = 78.21 RR22 x R = 13.03 x R = 13.03 RR3 3 == 13.0313.03 R = 2.35R = 2.35

Using the Radius, find the height. R = 2.35 2.352 x H x π = 245.7π = 245.7 H = about 14.2.H = about 14.2.

Calculating the Total Surface area of Calculating the Total Surface area of the cylinder.the cylinder. (2.35(2.3522xπx 2) + (2.35x2xπx14.2) = 227.02xπx 2) + (2.35x2xπx14.2) = 227.02 227.02 x 14 = Cost of the Metal Sheet227.02 x 14 = Cost of the Metal Sheet Metal sheet cost = $3421.6Metal sheet cost = $3421.6

Calculating the Concrete volume.Calculating the Concrete volume. Concrete would have 0.5 meters added to the original Concrete would have 0.5 meters added to the original

container. the concrete’s radius = 2.85 height = 0.2container. the concrete’s radius = 2.85 height = 0.2 Volume of concrete = 2.85Volume of concrete = 2.8522 x π x 0.2 = 5.1 x π x 0.2 = 5.1 Cost of concrete = 5.1 x 640 = $3264Cost of concrete = 5.1 x 640 = $3264

THE TOTAL COST = $3421.6+$3264 = THE TOTAL COST = $3421.6+$3264 = $6685.6$6685.6

http://images.google.com/images?gbv=2&&hl=en&newwindow=1&q=rice+storage&&sa=N&start=54&ndsp=18

http://www.dengie-crops.com/media/silos%20and%20lorry.JPG

What we found out What we found out in our research?in our research?

One adult eats .25kg of rice per One adult eats .25kg of rice per mealmeal

If there are 4 people in the If there are 4 people in the family, even though the children family, even though the children wouldn’t eat as much as adults, wouldn’t eat as much as adults, but we will just make it 1kg for a but we will just make it 1kg for a family, in case extras members, family, in case extras members, and food supply.and food supply.

1x50x14=700kg1x50x14=700kg

What is it the best solution?What is it the best solution?

Radius: 0.3mRadius: 0.3m Base area: 0.3m^2 (3.14x0.3^2)Base area: 0.3m^2 (3.14x0.3^2) Height: 3.5mHeight: 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^2TSA: 6.9m^2 Cost of metal: $97.3Cost of metal: $97.3 Concrete:0.2mConcrete:0.2m Concrete cost: $144.8Concrete cost: $144.8 Total cost: Total cost: $242$242

Why is it the best solution?Why is it the best solution?

Cylinder because it has the largCylinder because it has the largest area with a fixed perimeter.est area with a fixed perimeter.

Takes up all the rice we need wiTakes up all the rice we need without wasting a lot of volumes athout wasting a lot of volumes and money.nd money.

How we found the solution How we found the solution (justification)?(justification)?

Cylinder Cylinder 700kg goes into 700000cm^3700kg goes into 700000cm^3 Which = 0.7m^3Which = 0.7m^3 radius^2 x pi x height = 0.7radius^2 x pi x height = 0.7 height is diameter x 3height is diameter x 3 diameter is 2xradiusdiameter is 2xradius Therefore height= radius x 2 x 3Therefore height= radius x 2 x 3

radius^2 x radius x 2 x 3 x pi=0.7radius^2 x radius x 2 x 3 x pi=0.7 Radius^2x radiusx2x3=0.7/piRadius^2x radiusx2x3=0.7/pi≈0.22≈0.22 Radius^2x Radius =0.22/6 ≈0.037Radius^2x Radius =0.22/6 ≈0.037 radius^3=0.037radius^3=0.037 Radius=0.3Radius=0.3

Citation Citation Mathematics: water and grain storage facility projectMathematics: water and grain storage facility project. 30 Nov. 2008 . 30 Nov. 2008

<http://www.uswitch.com/water/ how-much-water-use/>.<http://www.uswitch.com/water/ how-much-water-use/>. Mathematics: water and grain storage facility projectMathematics: water and grain storage facility project. 30 Nov. 2008 . 30 Nov. 2008

<http://blog.naver.com/leemail07?<http://blog.naver.com/leemail07?Redirect=Log&logNo=40034391615>. Redirect=Log&logNo=40034391615>.

Mathematics: water and grain storage facilityMathematics: water and grain storage facility. 30 Nov. 2008 . 30 Nov. 2008 <http://www.querycat.com/faq/ <http://www.querycat.com/faq/ f4c59fee94b30846229276c79121f335>.f4c59fee94b30846229276c79121f335>.

Mathematics: water and grain storage facility projectMathematics: water and grain storage facility project. 30 Nov. 2008 . 30 Nov. 2008 <http://wiki.answers.com/Q/How_many_ml_of_water_does_a_person_<http://wiki.answers.com/Q/How_many_ml_of_water_does_a_person_need_a_day>. need_a_day>.

Mathematics: water and grain storage facility projectMathematics: water and grain storage facility project. 30 Nov. 2008 . 30 Nov. 2008 <http://www.hc-sc.gc.ca/fn-an/ food-guide-aliment/basics-base/quantit-<http://www.hc-sc.gc.ca/fn-an/ food-guide-aliment/basics-base/quantit-eng.php>.eng.php>.

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 projectMathematics: water and grain storage facility project. 30 Nov. 2008 . 30 Nov. 2008

<http://www.data360.org/ dsg.aspx?Data_Set_Group_Id=757<http://www.data360.org/ dsg.aspx?Data_Set_Group_Id=757>. >. Mathematics: water and grain storage facilty projectMathematics: water and grain storage facilty project. 30 Nov. . 30 Nov.

2008 <www.snopes.com/medical/myths/ 2008 <www.snopes.com/medical/myths/ 8glasses.asp>. 8glasses.asp>.