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ADD MATHS

PROJECT

POPCORN

(TASK II)

NAME LEVINTHRAN A/L KURUPARAM

CLASS 5K

ANGKA GILIRAN

I.C NO. 971211-56-5645

TEACHER MS KEE LAI YEE

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CONTENTS

NO. TITLE PAGE1 Acknowledgement 2

2 What is Popcorn 3

3 Objectives 4

4 Section A Questions 5

5 Section A Answers 7

6 Section B Questions 11

7 Section B Answers 13

8 Conclusion 20

9 Reflection 22

10 Reference 24

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ACKNOWLEDGEMENT

First of all, I would like to express my special thanks of gratitude to my additional mathematics

teacher, Miss Kee Lai Yee who allowed me the opportunity to do this project and provided me

assistance throughout finishing this project. Without her guide, I could not have finished my project

properly.

Secondly, I would like to extend my appreciation to my parents and my family for providing

everything, such as money to buy anything that are related to this project and their advice, which

was very important to do this project. I am grateful for their constant support and help.

Not forgotten to my friends who have contributed lots of ideas in finding the topic that would be

interesting to do and gave their comments on my research. I really appreciate their kindness and

help.

Last but not least, I would like to express my gratefulness to those who are involved either directly

or indirectly in completing this project. Thank you for all the assistance given.

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What is Popcorn

Popcorn, also known as popping corn, is a type of corn that expands from the kernel and puffs up

when heated. Popcorn is able to pop because, like amaranth grain, sorghum, quinoa, and millet, its

kernels have a hard moisture-sealed hull and a dense starchy interior. Pressure builds inside the

kernel, and a small explosion (or "pop") is the end result. Some strains of corn are now cultivated

specifically as popping corns.

There are various techniques for popping corn. Along with prepackaged popcorn, which is generally

intended to be prepared in a microwave oven, there are small home appliances for popping corn.

These methods require the use of minimally processed popping corn.

A larger-scale, commercial popcorn machine was invented by Charles Cretors in the late 19th

century.

Unpopped popcorn is considered nonperishable and will last indefinitely if stored in ideal

conditions.

Depending on how it is prepared and cooked, some consider popcorn to be a health food, while

others caution against it for a variety of reasons. Popcorn can also have non-food applications,

ranging from holiday decorations to packaging materials.

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OBJECTIVES

Apply and adapt a variety of problem-solving strategies to solve routine and non-routine

problems.

Acquire effective mathematical communication through oral and writing, and to use the

language of mathematics to express mathematical ideas correctly and precisely.

Increase interest and confidence as well as enhance acquisition of mathematical knowledge and

skills that are useful for career and future undertakings.

Realize that mathematics is an important and powerful tool in solving real-life problems and

hence develop positive attitude towards mathematics.

Train students not only to be independent learners but also collaborate, to cooperate, and to

share knowledge in an engaging and healthy environment.

Use technology especially the ICT appropriately and effectively.

Train students to appreciate the intrinsic values of mathematics and to become more creative

and innovative.

Realize the importance and the beauty of mathematics.

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SECTION A

QUESTIONS

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Questions

For this activity, you will be comparing the volume of 2 cylinders created using the same sheet of paper. You will be determining which dimension can hold more popcorn. To do this, you will have to find a pattern for the dimensions for the containers.

Materials :

8.5 x 11 in. white paper, 8.5 x 11 in. colored paper, tape, popcorn plate, cup, ruler1.

1. Take the white paper and roll it up along the longest side to form a baseless cylinder that is tall and narrow. Do not overlap the sides. Tape along the edges. Measure the dimensions with a ruler and record your data below and on the cylinder. Label “Cylinder A”.

Take the colored paper and roll it up along the shorter side to form a baseless cylinder that is short and stout. Do not overlap the sides. Tape along the edge. Measure the height and diameter with a ruler and record you data below and on the cylinder. Label it“Cylinder B”.

2. Do you think the two cylinders will hold the same amount? Do you think one will hold more than the other? Which one? Why?

3. Place Cylinder B on the paper plate with Cylinder A inside it. Use your cup to pour popcorn into Cylinder A until is full. Carefully, lift Cylinder A so that the popcorn falls into Cylinder B. Describe what happened. Is Cylinder B full, not full or over flowing?

4. As you share your popcorn snack, answer the questions below.

a) Was your prediction correct? How do you know?

b) If your prediction is incorrect, describe what actually happened?

5. a) State the formula for finding the volume of a cylinderb) Calculate the volume of Cylinder A.c) Calculate the volume of Cylinder B.d) Explain why the cylinders do or do not hold the same amount. Use the formula for the

formula for the volume of a cylinder to guide your explanation.

6. Which measurement impacts the volume more : the radius or the height? Work through the example below to help you answer the question. Assume that you have a cylinder with a radius of 3 inches and a height of 10 inches. Increase the radius by 1 inch and determine the new volume. Then using the original radius, increase the height by 1 inch and determine the new volume.Which increased the dimension had a larger impact on the volume of the cylinder? Why do you think this is true?

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SECTION A

ANSWERS

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Question 1

DIMENSION CYLINDER A (Inch) CYLINDER B (Inch)

HEIGHT 11.0 8.5

DIAMETER 2.6 3.4

RADIUS 1.3 1.7

Question 2

The two cylinders will hold different amounts. Cylinder B will hold more than Cylinder A. This is

because the radius of Cylinder B is longer and this make the volume is bigger than Cylinder A.

Although the height of Cylinder B is shorter than Cylinder A, but this does not affect much

compared to the effect of difference in radius.

Question 3

Cylinder B is not full. There is still space in the cylinder for more popcorn.

Question 4

Yes, the prediction is correct. It is based on the formula, volume of cylinder equals to 77.2 inch 3

According to the formula, radius, r has more effect than height,h since radius, r is squared. Thus, the

Cylinder B with greater radius, r have the greater volume, V than Cylinder A.

Cylinder B has a greater volume than Cylinder A.

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Question 5

a)

b)

c)

d) The cylinders have different radius and heights, therefore the volumes are different.

Question 6

CYLINDER RADIUS (Inch) HEIGHT(Inch) VOLUME (Inch3)

ORIGINAL 3 10 282.7

INCREASED RADIUS 4 10 502.7

INCREASED HEIGHT 3 11 311

The increase in volume is greater when there is an increase in the radius compared to an increase in the height. This is because the radius is squared when obtaining the volume and not the height. Therefore a change in the radius is more significant than a change in the height.

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Graph of Volume against Radius (Height = 10 inches)

Graph of Volume against Height (Radius = 3 inches)

Hence, based on both graphs, a change in the radius is more significant than a change in the height.

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SECTION B

QUESTIONS

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Question

If you were buying popcorn at the movie theatre and wanted the most popcorn, what type of

container would you look for?

Clue : You need more than one type of containers.

You are given 300 cm² of thin sheet material. Explain the details.

Have a thought about:

i. You are the popcorn seller, what type of container would you look for ?

ii. You are the producer of the containers. Which type of container would you choose to have the

most profit.

Method of Answering.

i. Five different container shape are chosen - Cube, Hemisphere, Cuboid, Cylinder and Cone

ii. Given that the total surface area of each of these containers is 300 cm2, the maximum value for

the container’s radius, length or height (whichever is most appropriate) is found using

differentiation.

iii. Based on the value found, the volume of the container is calculated and tabulated.

iv. A graph of volume against the container shape is drawn.

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SECTION B

ANSWERS

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Cube

Hemisphere

l

l

l

r

15

Cuboid

l

hl

16

Cylinder

h

r

17

Cone

hs

r

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Tabulation

CONTAINERHEIGHT

(cm)RADIUS

(cm)LENGTH

(cm)WIDTH

(cm)VOLUME

(cm3)

CUBE 7.7460 - 7.7460 7.7460 464.76

HEMISPHERE - 6.909 - - 690.99

CUBOID 5.0 - 10 10 500.00

CYCLINDER 5.6419 5.6419 - - 564.19

CONE 15.957 5.642 - - 531.92

Graph of Volume Against Container Shape

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Therefore, if I were buying popcorn at the movie theatre, I will choose the HEMISPHERE container because it can contain the most popcorn and hence, I can get the most amount of popcorn at one short. It helps me save money.

I. If I was the popcorn seller, I would use the CUBE container because it can contain the least amount of popcorn so that I could maximize my profit.

II. If I was the producer of the containers, I would choose the CYLINDER because it is the simplest to manufacture and would reduce the production cost. This increases the profit. Also this container has a large volume therefore it’ll be a popular choice among consumers.

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CONCLUSION

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Conclusion

From this project, I have learned to determine the volume of containers of different shapes. I have also learned that in a cylinder container, the radius of the cylinder affects the volume more than the height of the cylinder container.

This project taught me to economise when selecting a product. In this case, if we wanted the most popcorn, go for the hemisphere container.

However, from this project, I also learnt that to be wise in the manufacturing of these containers to avoid wastage of money and resources. Given that although the surface area of each container is the shape, their volumes are different. We must consider the shape of the container to be manufactured as it affects the cost for manufacturing it. Hence, this shows that we should put the knowledge that we have learnt in Add Maths to good use as it can benefit us in our daily lives.

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REFLECTION

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Reflection

Based on this project, I have realised that I have a good understanding of the Add Maths subject. However now that I have seen its application in real-life situations, I appreciate it a lot more and have renewed interest in the subject.

In addition to that, I realize that the Add Maths subject requires continuous practise to fully grasp whatever you are learning. Besides that solving Add Maths problems has made me solve problems more systematically and analytically.

Moreover it helps to make oneself more patient in solving problems as rushing through solutions will increase the probability of errors and careless mistakes. Indirectly, I am very thankful to have learnt this subject under the guidance of my teacher, Ms.Kee whom has diligently and patiently ensured that we understand the syllabus.

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Reference

1. http://en.wikipedia.org/wiki/Popcorn

2. SUCCESS Additional Mathematics Reference Book

3. http://www.math.com/tables/geometry/volumes.htm