CJ Developments

Our ProcessResearchConsolidationAnswers

How many people in a family?2.61 children born/woman (CIA World

Factbook)Round 2.61 children to 3 childrenAdd 2 parentsEquals 5 people in a family!

However, our group mostly has 4 people in each family, so:4 ± 1 people in a family!

Starting QuestionsHow much water does each person use?What do we use water for? What is the best shape to store water in?

Answering QuestionsWhat do we use water for?

DrinkingBathingWashing (dishes, laundry)ToiletsCooking

Answering QuestionsHow much water does an average person

use?Internet research69.3 gallons per person for indoor purposes ()

laundry, shower, toilets, cooking, drinkingConvert into litres1 gallon = 3.78541178 litres

69.3 gallons ≈ 263 litres Leeway: 263 ± 2 litres

Answering QuestionsWhat 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

How to calculate Surface AreaSurface area of a cylinder is calculated by:

Closed (2πrh) + (2πr2) = 2πr(r+h)

Open 2πrh + πr2

When r = radius of the cylinder’s base circle

h = the height of the cylinder

r

h

How to calculate volumeThe volume of a cylinder that has a radius of

r:π × r2 × hSince a cylinder is a prism, the

volume = base area × height

r

h

CalculationTotal 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 m3

This way, both the different sizes of family and different consumption of water are accounted for

Maximum 756.4m3 (around 757m3)Minimum716.4m3 (around 717m3)

Best Choice (Max. Volume)Radius (m)

Base Area (m2)

Height (m)SA of Height

(m2)Cost of Metal

($)Concrete (m3)

Concrete Cost ($)

Total Cost ($)

1 3.14 240.96 1514.00 21283.96 1.41 904.78 22189

2 12.57 60.24 757.00 10949.86 3.93 2513.27 13463

3 28.27 26.77 504.67 7857.01 7.70 4926.02 12783

4 50.27 15.06 378.50 6706.43 12.72 8143.01 14849

5 78.54 9.64 302.80 6438.31 19.01 12164.25 18603

6 113.10 6.69 252.33 6699.39 26.55 16989.73 23689

7 153.94 4.92 216.29 7338.27 35.34 22619.47 29958

8 201.06 3.77 189.25 8279.23 45.40 29053.45 37333

9 254.47 2.97 168.22 9480.24 56.71 36291.68 45772

10 314.16 2.41 151.40 10916.06 69.27 44334.16 55250

Radius vs. Height vs. Total CostRadius (m) Height (m) Total Cost ($)

1 240.96 219642 60.24 130773 26.77 122364 15.06 141425 9.64 177346 6.69 226607 4.92 287678 3.77 359829 2.97 4426010 2.41 53577

Best Choice (Min. Volume)Radius (m)

Base Area (m2)

Height (m)SA of Height

(m2)Cost of Metal

($)Concrete

(m3)Concrete Cost

($)Total Cost

($)

1 3.14 228.23 1434.00 20163.96 1.41 904.78 21069

2 12.57 57.06 717.00 10389.86 3.93 2513.27 12903

3 28.27 25.36 478.00 7483.68 7.70 4926.02 12410

4 50.27 14.26 358.50 6426.43 12.72 8143.01 14569

5 78.54 9.13 286.80 6214.31 19.01 12164.25 18379

6 113.10 6.34 239.00 6512.73 26.55 16989.73 23502

7 153.94 4.66 204.86 7178.27 35.34 22619.47 29798

8 201.06 3.57 179.25 8139.23 45.40 29053.45 37193

9 254.47 2.82 159.33 9355.80 56.71 36291.68 45647

10 314.16 2.28 143.40 10804.06 69.27 44334.16 55138

Radius vs. Height vs. Total CostMaximum Volume Minimum 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

JustificationViability 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 waterLevel of Accuracy (nearest whole number):

Easier to see the difference between figures

JustificationFor the cheapest cost,

the height of the cylinder will be at least 25m, which is too highWater pressure

For stability, if the radius is 1m larger, the height goes down by almost 10mStability, pressure

distribution

Our Storage TankHas a capacity of

7437 000 ± 200 000L

Is in the shape of a cylinder

Dimensions:Radius: 4 metresHeight: 14.5 ± 0.5

metresCost: $14700 ± 150

How did we get our numbers?Base area: π × r2

Height: Volume needed (m3) ÷ base areaTotal surface area: 2πr(r+h)Cost of metal: $ (14 × total surface area)Volume of concrete: (radius + 0.5m)2 × 0.2mCost of concrete: $ (640 × volume of

concrete)Total cost: $ (Cost of metal + cost of

concrete)

Starting QuestionsWhat 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?

Answering QuestionsWhat kind of grain are we storing?

Grain can be used to make many types of foodRice, corn, oats, ryeBread

for our purposes, we’ll pretend that we’re storing rice

Answering QuestionsHow 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 300cm3 of cooked rice per meal

300cm3 of cooked rice ≈ 100cm2 of uncooked rice

Answering QuestionsWhat kind of shape is best for storing the

grain?Real life examplesCylinder has the largest area for a fixed

perimeterCylinders are also used for silos

Examples of Grain Storage

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

http://www.mawaterquality.org/gallery/photos/hog%20grain%20storage.jpg

Calculation100cm3 uncooked rice × 3 meals × 4 people ×

50 families × 14 days = 840 000 cm3 of uncooked rice

840 000cm3 = 0.84m3

Shed has to have a volume of 0.84m3

round to 1m3

Best Choice for Grain StorageRadius Base Area Height

Circumference

SA of Height

TSACost of Metal

ConcreteConcrete

CostTotal Cost

0.1 0.03 31.8 0.6 20.0 20.0 280.4 0.1 64.3 345

0.2 0.1 8.0 1.3 10.0 10.1 141.8 0.2 100.5 242

0.3 0.3 3.5 1.9 6.7 6.9 97.3 0.2 144.8 242

0.4 0.5 2.0 2.5 5.0 5.5 77.0 0.3 197.0 274

0.5 0.8 1.3 3.1 4.0 4.8 67.0 0.4 257.4 324

0.6 1.1 0.9 3.8 3.3 4.5 62.5 0.5 325.7 388

0.7 1.5 0.6 4.4 2.9 4.4 61.6 0.6 402.1 464

0.8 2.0 0.5 5.0 2.5 4.5 63.1 0.8 486.6 550

0.9 2.5 0.4 5.7 2.2 4.8 66.7 0.9 579.1 646

1.0 3.1 0.3 6.3 2.0 5.1 72.0 1.1 679.6 752

Justification

With radius of 0.2 the height have to be 8 to hold 0.84m3.

To have a structure with stability have to be radius of 0.3 and height of 3.5.

JustificationHaving 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

Our Grain SiloIs cylindricalHas a capacity of 1m3

Dimensions:

Cost:Of metal sheet: $100 ± 10 ($97.30)Of concrete: $150 ± 10 ($144.80)Total cost: $250 ± 20 ($242.10)

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 <http://www.newsobserver.com/weather/drought/story/1016009.html>.

:https://www.cia.gov/library/publications/the-world-factbook/. 1 Dec. 2008 <https://www.cia.gov/ library/publications/the-world-factbook/>.

Where we got the image of grain storage: http://www.dengie-crops.com/media/silos%20and%20lorry.JPG. 1 Dec.

2008 <http://www.dengie-crops.com/media/silos%20and%20lorry.JPG>.

: http://www.mawaterquality.org/gallery/photos/hog%20grain%20storage.jpg. 1 Dec. 2008 <http://www.mawaterquality.org/gallery/photos/hog%20grain%20storage.jpg>.