additnal matheatics popcorn project

8/10/2019 additnal matheatics popcorn project

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CONTENTS

NO TOPICS PAGE

1. Title of projects

2. Introduction

3. Acknowledgement

4. History

5. Objective

6. Section A

7. Section B

8. Conclusion

9. Reflection


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INTRODUCTION


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ACKNOWLEDGEMENT

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

additional mathematics teacher, Puan Tan Gien Pei who gave me the

opportunity to do this project and help me a lot throughout finishing this project.

Without her guide, I may not finish my project and do it properly.

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

everything, such as money to buy anything that are related to this project andtheir advises, which is the most needed to do this project. I am grateful for their

constant support and help. Not forgotten to my friends who have contributed

lots of idea in finding the topic that would be interesting to do and gave their

comments on my research. I really appreciate their kindness and help.

Beside that, I want to thanks to the respondents for helping and spending

their time to answer my questions for this project. Without respondents, I mightnot be able to complete this project because their co-operation in answering the

questions, I have the conclusion for this project.

Last but not least, I would like to express my thankfulness to those who

are involved either directly or indirectly in completing this project. Thank you

for all the co-operation given.


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HISTORY of POPCORN

Popcorn was first discovered thousands of years ago byNative

Americans.It is one of the oldest forms of corn: evidence of popcorn from 3600

B.C. was found in New Mexico and even earlier evidence dating to perhaps as

early as 4700 BC was found in Peru. Some Popcorn has been found in early

1900s to be a purple color.

The English who came to America in the 16th and 17th centuries learned

about popcorn from the Native Americans.

During theGreat Depression,popcorn was comparatively cheap at 510

cents a bag and became popular. Thus, while other businesses failed, the

popcorn business thrived and became a source of income for many struggling

farmers. DuringWorld War II,sugarrationsdiminishedcandyproduction,

causing Americans to eat three times as much popcorn than they had before.

At least six localities (all in theMidwestern United States) claim to be

the "Popcorn Capital of the World":Ridgway, Illinois;Valparaiso, Indiana;Van

Buren, Indiana;Schaller, Iowa;Marion, Ohio;andNorth Loup, Nebraska.

According to theUSDA,most of thecorn used for popcorn production is

specifically planted for this purpose; most is grown inNebraska andIndiana,with increasing area inTexas.

As the result of anelementary schoolproject, popcorn became the

official state snack food ofIllinois,U.S.A.
http://en.wikipedia.org/wiki/Indigenous_peoples_of_the_Americashttp://en.wikipedia.org/wiki/Indigenous_peoples_of_the_Americashttp://en.wikipedia.org/wiki/Great_Depressionhttp://en.wikipedia.org/wiki/World_War_IIhttp://en.wikipedia.org/wiki/Rationing#United_Stateshttp://en.wikipedia.org/wiki/Rationing#United_Stateshttp://en.wikipedia.org/wiki/Candyhttp://en.wikipedia.org/wiki/Midwestern_United_Stateshttp://en.wikipedia.org/wiki/Ridgway,_Illinoishttp://en.wikipedia.org/wiki/Valparaiso,_Indianahttp://en.wikipedia.org/wiki/Van_Buren,_Indianahttp://en.wikipedia.org/wiki/Van_Buren,_Indianahttp://en.wikipedia.org/wiki/Schaller,_Iowahttp://en.wikipedia.org/wiki/Marion,_Ohiohttp://en.wikipedia.org/wiki/North_Loup,_Nebraskahttp://en.wikipedia.org/wiki/United_States_Department_of_Agriculturehttp://en.wikipedia.org/wiki/Cornhttp://en.wikipedia.org/wiki/Nebraskahttp://en.wikipedia.org/wiki/Indianahttp://en.wikipedia.org/wiki/Texashttp://en.wikipedia.org/wiki/Elementary_schoolhttp://en.wikipedia.org/wiki/Illinoishttp://en.wikipedia.org/wiki/Illinoishttp://en.wikipedia.org/wiki/Elementary_schoolhttp://en.wikipedia.org/wiki/Texashttp://en.wikipedia.org/wiki/Indianahttp://en.wikipedia.org/wiki/Nebraskahttp://en.wikipedia.org/wiki/Cornhttp://en.wikipedia.org/wiki/United_States_Department_of_Agriculturehttp://en.wikipedia.org/wiki/North_Loup,_Nebraskahttp://en.wikipedia.org/wiki/Marion,_Ohiohttp://en.wikipedia.org/wiki/Schaller,_Iowahttp://en.wikipedia.org/wiki/Van_Buren,_Indianahttp://en.wikipedia.org/wiki/Van_Buren,_Indianahttp://en.wikipedia.org/wiki/Valparaiso,_Indianahttp://en.wikipedia.org/wiki/Ridgway,_Illinoishttp://en.wikipedia.org/wiki/Midwestern_United_Stateshttp://en.wikipedia.org/wiki/Candyhttp://en.wikipedia.org/wiki/Rationing#United_Stateshttp://en.wikipedia.org/wiki/World_War_IIhttp://en.wikipedia.org/wiki/Great_Depressionhttp://en.wikipedia.org/wiki/Indigenous_peoples_of_the_Americashttp://en.wikipedia.org/wiki/Indigenous_peoples_of_the_Americas


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OBJECTIVESApply and adapt a variety of problem-solving strategies ti 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


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Materials :

8.5 x 11 in Green paper

11 x 8.5 in Blue paper

Tape

Popcorn plate

Cup

Ruler

1. Cylinder A.

2. Cylinder B.

8.5

11

11

8.5


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ANSWER 1

DIMENSION CYLINDER A CYLINDER B

HEIGHT 11.0 8.5

DIAMETER 2.6 3.4RADIUS 1.3 1.7

11

2.7

1.3

8.5

3.5

1.7

HEIGHT DIAMETER RADIUS

Dimension of Cylinder

CYLINDER ACYLINDER B


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ANSWER 2

The two cylinders will hold the different amount. 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 doesnot affect much compare the affect of different in radius.

ANSWER 3

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

ANSWER 4a) Yes, my prediction is correct. It is based on the formula, volume of cylinder equals to

. According to the formula, radius,r has more effect than height,hsince radius,ris

squared. Thus, the Cylinder B with greater radius,rhave the greater volume,V than

Cylinder A.

b) Cylinder B has a greater volume than Cylinder A.


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ANSWER 5

a)An element of volume, is a right cylinder of base areaAwisquare units and a

thickness of ixunits. Thus if Vcubic units is the volume of the rightcircular cylinder, byRiemann sums,

Using cylindrical coordinates, the volume can be calculated by integration over

=

b)

Volume of Cylinder A

V =

= x 1.3 x 11

= 58.4 cm

c) Volume of Cyliinder B

V = h

= x 1.7 x 8.5

= 77.2 cm
http://en.wikipedia.org/wiki/Riemann_sumshttp://en.wikipedia.org/wiki/Riemann_sumshttp://en.wikipedia.org/wiki/Riemann_sumshttp://en.wikipedia.org/wiki/Riemann_sums


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d)

Different cylinders with different radii and height will have different values

in volume. Based on the formula,, the radius is squared and hence

radius plays a bigger part than the diameter. The reason why Cylinder B has

bigger volume than Cylinder A because it has a bigger radius than Cylinder A


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Data and Observations:

The cylinder with have the greater radius and diameter will have the greater volume

The radius of Cylinder B is greater than Cylinder A.

The volume of Cylinder B is greater than Cylinder A.

So, Cylinder B holds more popcorn than Cylinder B.

DIMENSION CYLINDER A CYLINDER B

HEIGHT, inch 11.0 8.5DIAMETER, inch 2.6 3.4

RADIUS, inch 1.3 1.7

VOLUME, inch 58.4 77.2

Height,h Diameter,d Radius,r Volume,V

Cylinder A 11 2.6 1.3 58.4

Cylinder B 8.5 3.4 1.7 77.2

0

10

20

30

40

50

60

70

80

90


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ANSWER 6

Original ;

RADIUS HEIGHT VOLUME3 10 282.74

Increased Radius ;

RADIUS HEIGHT VOLUME

4 10 502.65

5 10 785.40

6 10 1130.977 10 1539.38

8 10 2010.62

Increased Height ;

RADIUS HEIGHT VOLUME

3 11 311.02

3 12 339.293 13 367.57

3 14 395.84

3 15 424.12

From the tables above, it is clear that the radius lays a larger impact on the

volume of the cylinder. This is because the radius is squared in the formula, to

determine volume of the cylinder. Increasing the radius increased the volumemore than increasing the height. Therefore the radius is squared to find the

volume, which increases its impact on the volume.


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CONCLUSIONContainer Height Radius Length Width Volume

CUBE 7.7460 - 7.7460 7.7460 464.76

HEMISPHERE - 6.9090 - - 690.99

CUBOID 5.00 - 10.00 10.00 500.00

CYLINDER 5.6419 5.6419 - - 564.19

CONE 10.5006 7.4252 - - 606.03

Shape of containers that give the most popcorn reflect the

maximum volume. From the activity earlier, I found that increasing the radius

increased the volume more than increasing the height. This is because the radius

is squared to find the volume, which increases its impact on the volume.

From the calculations, it has been found that HEMISPHEREcan

be filled in with the most amount popcorn. It followed by CONE, CUBOID,

and CYLINDER. These means that CUBEis the container that can be filled

with the least amount of popcorn.

Randomly, surveying at the movie theater, no CUBE or CUBOID

shapes can be found. Therefore, in this case, the HEMISPHEREwas the most

preferable container that can have the most popcorns.


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

If I was the popcorn seller, I will look for CUBE shape container. It is because

the least popcorns will be in. So, I will get the most profit for my sale.

Furthermore, it is cute and simple shape.

ii.You are the producer of the containers, what type of container would you

choose to have the most profit?

If I was the producer of the popcorns containers, I will look for CONE shape

container. It is because this shape is the easiest production and it takes less effort

and also no time consuming to produce.


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Cube

Hemispher

e

Cuboid

Cylinder

Cone

464.76

690.99

500

564.19

606.03

Volume of container,V (cm)

Volume of container


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REFLECTIONIn the making of this project, I have spent countless hours doing this project. I

realized that this subject is a compulsory to me. Without it, I cant fulfill my big

dreams and wishes. This project taught me to economise when selecting a

product. In this case, if we wanted the most popcorn, go for the cylinder

container However, from this project, we also learn that we must be wise in

handling manufacture of these containers to avoid wastage and harm towards

environment. We must also consider the shape of the container to bemanufactured as it affects the cost for manufacturing it. Hence, this shows that

we, as humans are gifted with minds to think and plan ahead for a better future.

I used to hate Additional Mathematics

It always make me wonder why this subject is so difficult

It always an absolute obstacle for me

Throughout day and night

Isacrificed my precious time to have fun

From

Monday, Tuesday, Wednesday, Thursday, Friday,,,

And even the weekend that I always looking forward to

From now on, I will do my best on every second that I will learn Additional

Mathematics full of effort!

additnal matheatics popcorn project

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