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ADD MATHS PROJECT DRINKS PACKAGING

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High School ADD MATHS SCHOOL PROJECT
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Contents No . Topic Page 1 Introduction 1-2 2 Part 1 3-5 3 Part 2 6-10 4 Part 3 11- 14 5 Further Exploration 15 6 Reflection 16
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Page 1: ADD MATHS PROJECT DRINKS PACKAGING

Contents

No. Topic Page

1 Introduction 1-2

2 Part 1 3-5

3 Part 2 6-10

4 Part 3 11-14

5 Further Exploration 15

6 Reflection 16

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INTRODUCTION

The history of packagingdrinks dates back as early as the 17th century. Back then, Waters from natural

springs were recognized as being safe (even healthy) to drink from earliest times and were transported

by wherever means that were available. Naturally carbonated waters were collected into earthenware

containers which were tightly sealed with cork and wax, usually not very successfully. The used of

earthenware bottles proved to be unsatisfactory for the more highly carbonated aerated mineral waters

and they were soon replaced by glass bottles.

Many of the early glass bottles had round bottoms ensuring that they were stored on their side,

thereby keeping the corks moist and so preventing leakage from corks drying out. The manufacture of

glass bottles was a skilled job as they were hand blown. Although some semi-automation had been

introduced earlier, the first patent for an automatic glass bottle blowing machine was granted to

Michael J. Owens in the USA in 1904.High pressure generated inside bottles by the carbonation

caused frequent leakage and although improved by wiring-in-place, corks were generally

unsatisfactorily. Many alternative forms of seals were patented over the years and these fell broadly

into three main categories:

Wire and rubber sealing devices were especially popular in the USA until the early 1900s. The wire

could be either an internal spring form, which held a seal in place on the inside of the neck, or of the

external ‘swing’ type, in which an external wire frame was used to hold a ceramic plug in place

against a rubber seal. First patented by Charles de Quillfeldt in 1874, this latter type is still currently

in use for some specialty.

Variations on the theme of using an internal ball made from rubber, ebonite or glass were developed

and used with varying degrees of success. The ball was held in place by the internal pressure. The

most successful of these was patented by Hiram Codd of London. His bottle was widely used in the

UK from 1870s until the 1930s. A similar bottle, but with a floating rubber ball acting as seal, was

patented in the USA by S. Twitchell in 1883.

The third popular alternative was the internal screw top bottle. Unlike today’s bottle, the thread was

on the inside of the bottle neck and an ebonite or wooden stopper screwed on to the neck, with a

rubber washer being used to improve the seal. These types of stoppers were in common usage well

into the 1950s in the UK. Ebonite, an early type of plastic resin material soon replaced wood, which

has a tendency to absorb moisture, causing it to swell and crack the bottle neck.

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A major step forward in sealing development was made by William Painter, who in 1895 patented the

‘Crown Cork’, founding the Crown Cork and Seal Company in 1 April 1892. Although initially slow

to gain acceptance for two reasons:

The existing large capital investment in returnable bottles and bottling plant, and

The need for a tool to remove the crown, the crown cork eventually became popular,

especially for small single serve and beer bottles. Screw stopper retained their popularity for the

larger bottles where re-sealability was important.

Except for specialty earthenware ginger beer containers, glass bottles were the only form of packaging

for carbonates for over hundred years until the introduction of cans in the 1960s. Then, just as the

second half of the nineteenth century had been the time for product development, the second half of

the twentieth century became the time for packaging and distribution of development.

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PART 1

a)

b)

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Types of packaged drinksBrands ManufacturerNestle-MILO Nestle Products Sdn. Bhd.Ribena GlaxoSmithKline Consumer

Healthcare Sdn Bhd

MARIGOLD Malaysia Milk Sdn. Bhd.Yeo’s Yeo HianSeng(M) Sdn. Bhd.Desa Milk Desa Cattle(S) Sdn. Bhd.Sabah Tea Sabah Tea Sdn. Bhd.

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Brand Picture Price (RM)

Pokka (330ml) 2.40

Drinho (200ml) 1.50

MARIGOLD-Orange(250ml)

1.50

YEO’S Chrysanthenum Tea(250ml)

1.50

Desa Milk(500ml)

3.50

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PART 2

(a) (i)

No. Types of drinks/Students Name

YEO’s Dairy Milk(DESA)

Marigold POKKA DRINHO

1 Alif Muazzam (Me)

/

2 Alden Lim /3 Alex Jong /4 Alicia Wee /5 Anjali /6 Betty Ng7 Chin Shin Yee / /8 Christal Fong9 Cyrus Soong10 Darren Lim /11 Dayangku Ayesha12 Farez Syazwan13 Ferinna Chin /14 Gary Chong15 Gregory Ho /16 Hannah Hidayati17 Irfan Yazid18 Joscelin Liew19 Julie D. /20 Kelvin Yong21 Kesavan22 Kevin Liau23 Kevin Lai /24 Kimberly Chong25 Alvin Lee26 Lo Janzen27 Luthais Tseu28 Maria Hannah29 Melvin Ling30 Mohd.Arsyad /31 Mohd.Naqiyuddin32 Mohd.Radzi33 Muhd.Adib34 Muhd.Yasrin 35 Nichola Chung /36 Nur Fatin Syafiqah

37 Oliver Law /38 Patricia Wee /39 Ridge Cromwell40 Sai Zen Zek /41 Seraj Chandran /42 Shareene Jasmine43 Siow Wei44 Syakir Hamdi45 Wilfredo 46 Wong Chen Sean /

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47 Yeoh Lei Ie48 Prince Nevin (5B)49 Joshua Ting (5B)

(b) (i)

(ii)

(iii) Conclusion: Milo is the most preferred packaged drinks among the 50 students.

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Types of drinks Number of students who prefer drink

PokkaDrinhoYeo's Dairy MilkMarigold Orange

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(c) (i)

Types of drinks Volume per serving, f

Sugar Content per ml, x

fx fx2

Drinho 200ml 0.070g/ml 14.000 0.98

Marigold Peel-Fresh Orange 250ml 0.106g/ml 26.500 2.809

Dairy Milk 250ml 0.042g/ml 10.500 0.441

Pokka 330ml 0.093g/ml 34.875 3.243

Yeo’s Soya Bean Milk 250ml 0.086g/ml 21.500 1.849

∑f = 1325 ∑fx = 107.375 ∑fx2 = 9.322

(ii)

Mean of sugar content = ∑fx/∑f

= 107.375/1325

= 0.081g/ml

Standard deviation = √[∑fx2/∑fx – (mean)2]

= √[9.322/1325 - (0.081)2]

= 0.022

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Effect of long term consumption of these packaging material to our health

Blood glucose levels

Sugar, because of its simpler chemical structure, may raise blood glucose levels more quickly than starch. This finding suggests that this basic differentiation between starch and sugar is insufficient reason to segregate these two substances for controlling blood glucose levels in diabetics, the idea behind carbohydrate counting. A more effective distinction could be that suggested by multiple meta-studies between free sugars and naturally-occurring sugars which suggest that they have different impacts on health.

Immune system

According to WebMD, consuming too much sugar suppresses the immune system.

Obesity and diabetes

Studies on the link between sugars and diabetes are inconclusive, with some suggesting that eating excessive amounts of sugar does not increase the risk of diabetes, although the extra calories from consuming large amounts of sugar can lead to obesity, which may itself increase the risk of diabetes. Others show correlation between refined sugar (free sugar) consumption and the onset of diabetes, and negative correlation with the consumption of fiber including a 2010 meta-analysis of eleven studies involving 310,819 participants and 15,043 cases of type 2 diabetes. This found that "SSBs (sugar-sweetened beverages) may increase the risk of metabolic syndrome and type 2 diabetes not only through obesity but also by increasing dietary glycemic load, leading to insulin resistance, β-cell dysfunction, and inflammation". As an overview to consumption related to chronic disease and obesity, the World Health Organization's independent meta-studies specifically distinguish free sugars ("all monosaccharides and disaccharides added to foods by the manufacturer, cook or consumer, plus sugars naturally present in honey, syrups and fruit juices") from sugars naturally present in food. The reports prior to 2000 set the limits for free sugars at a maximum of 10% of carbohydrate intake, measured by energy, rather than mass, and since 2002 have aimed for a level across the entire population of less than 10%. The consultation committee recognized that this goal is "controversial. However, the Consultation considered that the studies showing no effect of free sugars on excess weight have limitations."

Cardiovascular disease

A number of studies in animals have suggested that chronic consumption of refined sugars can contribute to metabolic and cardiovascular dysfunction. Some experts have suggested that refined fructose is more damaging than refined glucose in terms of cardiovascular risk. Cardiac performance has been shown to be impaired by switching from a carbohydrate diet including fiber to a high-carbohydrate diet.Switching saturated fatty acids for carbohydrates with high glycemic index values shows a statistically significant positive association with the risk of myocardial infarction. Other studies have found links between high fat and high glycemic index carbohydrates accelerates the development of cardiac pathology and pump dysfunction in hypertension despite no signs of diabetes and only a modest level of obesity, suggesting that the link between obesity and coronary heart disease should be shifted towards macronutrients and the high glycemic load typical of the "junk-food" diet.

The consumption of added sugars has been positively associated with multiple measures known to increase cardiovascular disease risk amongst adolescents as well as adults. Studies are suggesting that the impact of refined carbohydrates or high glycemic load carbohydrates are more significant than the

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impact of saturated fatty acids on cardiovascular disease. A high dietary intake of sugar (in this case, sucrose or disaccharide) can substantially increase the risk of heart and vascular diseases. According to a Swedish study of 4301 people undertaken by Lund University and Malmö University College, sugar was associated with higher levels of bad blood lipids, causing a high level of small and medium low-density lipoprotein (LDL) and reduced high-density lipoprotein (HDL). In contrast, the amount of fat eaten did not affect the level of blood fats. As a side note, moderate quantities of alcohol and protein were linked to an increase in the good HDL blood fat.

Alzheimer's disease

It is suggested that Alzheimer's disease is linked with the western diet. This is characterised by high intakes of red meat, sugary foods, high-fat foods and refined grains. It has been hypothesized that dementia could be prevented by the taking of mono-supplements of specific vitamins or drugs, but studies have shown that this approach does not show appreciable results.

Dietary pattern analysis considers overall eating patterns, comparing diets of people with Alzheimer's disease to diets of healthy controls using factor analysis. This analysis shows a major eating pattern for those with Alzheimer's characterised by a high intake of meat, butter, high-fat dairy products, eggs and refined sugar, while the major eating pattern for those without Alzheimer's was characterised by a high intake of grains and vegetables.

One group of experimenters compared a normal rodent diet (19% protein, 5% fat and 60% complex carbohydrate) with free access to water against the same diet but with free access to a 10% sucrose solution. The experimental results underscore the potential role of dietary sugar in the pathogenesis of Alzheimer disease and suggest that controlling the consumption of sugar-sweetened beverages may be an effective way to curtail the risk of developing the disease.

Macular degeneration

There are links between free sugar consumption and macular degeneration in older age.

Tooth decay

In regard to contributions to tooth decay, the role of free sugars is also recommended to be below an absolute maximum of 10% of energy intake, with a minimum of zero. There is "convincing evidence from human intervention studies, epidemiological studies, animal studies and experimental studies, for an association between the amount and frequency of free sugars intake and dental caries" while other sugars (complex carbohydrate) consumption is normally associated with a lower rate of dental caries.Lower rates of tooth decay have been seen in individuals withhereditary fructose intolerance.

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PART 3

(a) (i)

Length (cm) Width (cm) Height (cm) Amount of packaging material used (cm2)

5.0 5.000 10 250.0005.1 4.902 10 250.0405.2 4.808 10 250.1645.3 4.717 10 250.3405.4 4.630 10 250.6045.5 4.545 10 250.896

5.6 4.464 10 251.2765.7 4.386 10 251.7105.8 4.310 10 252.1965.9 4.237 10 252.736

(ii) Length = 5cm, width = 5 cm and height = 10cm.

(b) (i)

In mathematics and the arts, two quantities are in the golden ratio (φ) if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one.

Expressed algebraically:

where the Greek letter phi ( ) represents the golden ratio. Its value is:

(ii)

Length, x(cm) Width, 1.6x(cm) Height, h(cm) Amount of packaging material used (cm2)

5.1 8.16 6.007 175.6345.2 8.32 5.778 172.8905.3 8.48 5.562 170.2625.4 8.64 5.358 167.7435.5 8.80 5.165 165.3275.6 8.96 4.982 163.0095.7 9.12 4.809 160.7845.8 9.28 4.645 158.6465.9 9.44 4.489 156.5926.0 9.60 4.340 154.617

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(iii)

Calculation using differentiation,V = 2501.6x2h = 250h = 250/1.6x2

A = 2[1.6x2 + 1.6xh + xh]= 2[1.6x2 + 2.6xh]= 2[1.6x2 +2.6x(250/1.6x2)]= 3.2x2 +812.5/x

dA/dh = 6.4x – 812.5x-2

0 = 6.4x – 812.5x-2

= 6.4x3 – 812.5x3 = 812.5/6.4x = 5.031.6x = 8.05h = 250/1.6(5.03)2

= 6.18

*Length = 5.03cm, Width = 8.05cmand Height = 6.18cm.

(iv)

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(c)

Type of drink Dimension (Length × Width × Height) (cm)

Reason

Milo 5.00×5.00×10.00 Square base provides extra stability.

Pokka 4.17×4.00×15.00 Height is more obvious providing an interesting packaging.

Yeo’s Chrysanthemum Tea

4.00×5.00×12.50 Standard size for easy storage.

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FURTHER EXPLORATION

Total Surface Area :2πr2 + 2πrh= 2(π)(2)2+2(π)(2)(9.5)

= 144.5133cm2

Volume:

= (π)(2)2(9.5)= 119.3805cm2

Pro Con- Large volume- Easy to hold

- Not Stable

Total Surface Area:

= π[3(3+5)]= 75.3982

Volume:1/3 πr2h

= 1/3(π)(3)2(4)= 37.6991

Pro Con- Stable

- Attractive- Small Volume- Hard to hold

Total Surface Area:Base Area + Triangle

surface= 36 + 4[(3)(4)]

= 84

Volume:1/3 × Base Area × h

=1/3 × 36 × 4= 48

Pro Con

- Stable- Attractive

-Small Volume- Hard to hold

- Sharp edges and sides

Usual materials used to package drinks

Materials used for packaging consist mainly of petrochemical products, usually plastic, and also cartons made of paperboard. Plastic packaging can be massed produced but are difficult to decompose. Thousands of years are required for plastics to break down and in the process, may release poisonous toxic, thus polluting the environment. Therefore, cartons made of paperboard are bio-degradable and more environment friendly.

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REFLECTION

I have gained many valuable lessons throughout the project. This includes gaining knowledge on how

to carry out a good project. I realized that the planning stage is the most important part of the project

because any mistakes at this stage would jeopardize the whole assignment.

In order for the project to be successful, I collected information from the internet and brochures

pertaining to the types of packet drinks available in the market. I studied their shapes; height, width

and length. Then, based on my observation, I came up with my own design.

From another aspect, I realized the importance of sharing information with others. With reliable

friends, finding and sharing information helped me to complete the project successfully. My friends

and I discussed about the project and we shared ideas with one another. This discussion has made

me more confident to carry out future projects. Not only that, this experience has enabled me to

communicate with others effectively, thus enhancing my communication skills.

Finally, this project has taught me the importance of punctuality and carrying out proper research to

avoid plagiarism.

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