Additional Mathematics Project 2015

TITLE: Water Usage ReductionNAME: -IC NUMBER: -TEACHER IN CHARGE: - Introduction:In our modern era, water is greatly taken advantage of. People waste a great amount of water daily and do not even realize it. Some of those who do, dont even take action against it! However, there are many ways to save water. Of the many are rainwater collection and accumulation. Rainwater accumulation can help to save pipe water because the rain, too, is a source of water!Part I1. Total area of school garden: 690m22. a) Total volume of water used per day=1300students x 15litres + 690m2 x 2litres=20880litres=20.88m3b) Water expenditure per month =20.88 x RM1.2 x 22+RM551.233. a) Students:a=1300r=103/100 = 1.03

T11 = 1300 x 1.0310 = 1747.1 = 1747 Students (Rounded off to the nearest student)

Water Usage:a=15r=1.05

T11 = 15 x 1.0510 = 24.43litres

Amount of water used in 2024 =1747 x 24.43litres = 42679.21litres b) Number of students Assume the number of students increases by 3% yearly. Year20142015201620172018201920202021202220232024

Student number13001339137914211463150715521599164716961747

Students daily water usage Assuming water usage increases by 5% yearly. Year20142015201620172018201920202021202220232024

Water Usage (litres)1515.7516.5417.3618.2319.1420.1021.1122.1623.2724.43

Students total daily water usage in the year 2024 = 1747 x 24.43 litres=42679.21 litres

Values obtained from the methods in 3.a) and 3.b).

c) I 24/14 = (Q2024/Q2014) x 100 = (42679.21 x 1900)/(19500 x 190) x 100 = 218.87

The amount of water used by the students in the year 2024 based on year 2014 has increased by 218.87%

Part II1. a)

b) Total Area of A,B,C,D,E,F,G,H,I,J,K= 5290.48 m2

Assuming all the roofs of the school buildings are attached with water tanks meaning to collect rainwater, Volume= 2.6 x 5290.48 =13755.25m3

13755.25m3 can be collected annually.

2. The volume of water used for 5 days is 20.88m3 x 5 = 104.4m3

3. i) Differentiation 104.4=r2h h = 104.4/r2

Area = 2rh + 2r2 = 2r(104.4/r2) + 2r2 = 208.8 r1 + 4r

dA/dr= 208.8/r2 + 4r

4r3 = 208.8 r3 = 2.55

Area = 208.8/2.55 + 2(2.55)2 = 122.74m2 Cost = 122.74 x 70 = RM 8591.80

Tabulation:

r/mh/mSurface Area/m2

0.0513292.624176.02

0.55109.86381.55

1.0530.14205.77

1.5513.83149.78

2.057.91128.29

2.555.11122.73

Minimal cost = 122.73 x 70 =RM8591.10Minimal cost is RM8591.10.

ii) Differentiation

104.4= l2hArea=2l2 + 4lh h = 104.4/l2 = 2l2 + 417.6l1

dA/dl = 4l 417.6/l2 4l = 417.6/l2 l3 = 104.4 l = 4.71 m

Area = 2(4.71)2 + 417.6/4.71 = 133.03 m2

Minimum cost= 133.03 x 7 = RM 9312.10

Tabulation:

l/cm h/mSurface Area/ m2

2.2121.38198.77

2.7114.22168.83

3.2110.13150.68

3.717.58140.02

4.215.89134.64

4.714.71133.03

Minimal cost = 133.10 x 70 = RM 9317Therefore, minimal cost is RM9317.

iii) Substitution 104.4=l3Area = 6l2 l = 4.71 m = 6(4.71)2 = 133.03 m2Minimal cost = 133.03 x 70 = RM 9312.1Tabulation:

l/cmSurface Area/ m2

2.2129.31

2.7144.06

3.2161.82

3.7182.58

4.21106.34

4.71133.10

Minimal cost = 133.1 x 70 = RM 9317Therefore the minimal cost is RM9317 4. Overall, the most suitable water tank shape would be the cylindrical shape. As it goes, a cylinder has a larger volume and less surface area compared to the cuboid shape. Thus, material used to construct the tank would also be less, making the tank less costly. A water tank with the shape of a cylinder is also much more stable comparatively. This is because edges create stress points. So having a water tank without stress points would greatly improve stability. Besides, cylindrical shaped tanks are much easier to maintain cleanliness compared to a cuboid shape for the corners are hard to clean. In conclusion, the best possible shape to use for a water tank in my school would be the cylindrical shape.

Further Exploration1. The cost of the cylinder is the cheapest at RM 8591. By comparing the cost of construction and expenditure that can be reduced from this rainwater harvesting, the project if practical. It will supply for the schools water demand and will aid in reducing the schools expenditure for water as well as contribute to water saving.

2. The harvesting of rainwater is the accumulation of rainwater so it can by used on site rather than letting it go to waste. This rainwater is used to water the plants in the school garden. It can also be used as washroom water supply. However, there are many problems that come with this as well. One of the greatest problem faced is the cleanliness of the water accumulated. Since we are living in hot country, mosquitoes and insects tend to breed everywhere. Accumulating this rainwater may become a breeding place for mosquitoes. Apart from that, water accumulated in such big tanks can be easily dirtied through the growth of moss or algae. Besides, the cost for the tanks used to accumulate the water also uses quite an amount of money. Since these tanks have to be of a good quality to withstand the heat from the sun, it is not cheap. Moreover, the rainwater collected is very dependent on rainfall. If the season were to be a dry season, water collection will be minimal! Therefore, although collecting rainwater has its perks, it also has its cons.

3. As it is, it is totally convenient for government buildings to make use of rainwater. Although at the start, the tanks are costly, in the long run, it can save a huge amount of water. This will reduce water cost and contribute to the environment simultaneously.

ConclusionThe collection of rainwater can greatly contribute to mankind. As it is, people have been simply using water and thoughtlessly wasting it. Clean water will soon become a rarity should no action be taken upon it. Therefore, saving water is a necessity. The accumulation of rainwater can help to save water. Instead of using fresh clean water to wash your car or water the flowers, rainwater is a better alternative. To saving water for the future generation, is to start saving now.