SEKOLAH MENENGAH KEBANGSAAN

SETAPAK INDAH

NAME : AIMAN BIN AHMAD NAZMICLASS : 5 SCIENCE 1IC NO. : 970424146175TEACHER : PUAN CHETHY QASMAWANTHY BINTI NOR AHAD

CONTENTS

NO. TOPIC PAGE

1 TITTLE

2 CONTENTS

3 ACKNOWLEDGEMENT

4 HISTORY

5 OBJECTIVE

6 SECTION A

7 SECTION B

8 CONCLUSION

9 REFLECTION

10 RUBRIC

ACKNOWLEDGEMENT

First of all, I would like to express my special thanks of gratitude to my additional mathematics teacher, Puan Cethy who gave me the opportunity to do this project and help mea 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 and their 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.

Last but not least, I would like to express my thankfulness to those who are involvedeither directly or indirectly in completing this project. Thank you for all the co-operation given

HISTORY OF POPCORN Popcorn was first discovered thousands of years ago by Native 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 the Great Depression, popcorn was comparatively cheap at 5 – 10 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. During World War II, sugar rations diminished candy production, causing Americans to eat three times as much popcorn than they had before.

At least six localities (all in the Midwestern United States)claim to be the "Popcorn Capital of the World": Ridgway, Illinois; Valparaiso, Indiana; Van Buren, Indiana; Schaller, Iowa; Marion, Ohio; and North Loup, Nebraska. According to the USDA, most of the corn used for popcorn production is specifically planted for this purpose; most is grown in Nebraska and Indiana, with increasing area in Texas.

As the result of an elementary school project, popcorn became the official state snack food of Illinois, U.S.A

OBJECTIVES

Apply 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.

SECTION A

QUESTION 1For this activity, you will be comparing the volume of 2 cylinders created using the same sheetof paper. You will be determining which dimension can hold more popcorn. To do this, youwill 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, ruler.

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

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

ANSWER 1

DIMENSION CYLINDER A CYLINDER B

HEIGHT 11.0 8.5

DIAMETER 2.6 3.4

RADIUS 1.3 1.7

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

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 thanCylinder A. Although the height of Cylinder B is shorter than Cylinder A, but this does notaffect much compare the affect of different in radius.

 

QUESTION 3Place 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?

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

  

QUESTION 4a) Was your prediction correct? How do you know?

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

ANSWER 4a) Yes, the prediction is correct. It is based on the formula,

volume of cylinder equals toπ r2h. According to the formula, radius,r has more effect than height,hsince radius,r issquared. Thus, the Cylinder B with greater radius,r have the greater volume,V thanCylinder A.

b) Cylinder B has a greater volume than CylinderA.

QUESTION 5a)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 theformula for the volume of a cylinder to guide your explanation.

ANSWER 5a) V=π r2 h

b) V=π r2 h

¿ π X 1.32 X 11 =58.4 inches3

c) V ¿ π r2h

=π X 1.72 X 8.5

=77.2inch3

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

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 11.0 8.5

DIAMETER 2.6 3.4

RADIUS 1.3 1.7

VOLUME 58.4 77.2

QUESTION 6Which 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.

CYLINDER RADIUS HEIGHT VOLUME

ORIGINAL

INCREASED RADIUS

INCREASED HEIGHT

Which increased the dimension had a larger impact on the volume of the cylinder? Why do you think this is true?

ANSWER 6CYLINDER RADIUS HEIGHT VOLUMEORIGINAL 3 10 282.7

INCREASED RADIUS

4 10 502.7

INCREASED HEIGHT

3 11 311

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.

SECTION B

 

QUESTIONIf you were buying popcorn at the movie theater 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.

 

CONCLUSIONCONTAINER HEIGHT RADIUS LENGTH WIDTH VOLUME

CYLINDER 5.64 5.64 - - 563.69CUBE 7.75 - 7.75 7.75 465.48

CUBOID 7.07 - 7.07 14.14 706.79CONE 10.51 7.42 - - 605.95

Shape of containers that give the most popcorn reflect the maximum volume from the height. From the activity earliar, I found that increasing the radius is squared to find the volume, which increase its impact on the volume. From the calculation, it has been found that the cuboid can be filled with the most amount of popcorn. It followed by coneand hexagon. These means that cube is 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 cuboid was most preferable container that can have the most popcorns.

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 cylinder shape container. It is because this shape is it easiest production and it takes the least effort and also no time consuming the produce

REFLECTIONIn the making of this project, I have spent countless hours doing this project. I realized that thissubject is a compulsory to me. Without it, I can’t fulfill my big dreams and wishes.

I used tohate Additional Mathematics… It always make me wonder why this subject is so difficult… It always an absolute obstacle for me… Throughout day and night… I sacrificed 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!

ANSWER1. Cylinder container

surface area =2πrh+π r2

h=300−π r2

2 πr

volume =π r2h

=π r2(300−π r2

2 πr )

maximum volume =dvdr =0

π r2(300−π r2

2 πr ) = ( 300 π r2−π r 4

2 πr )=( 300 π r2−π r 4

2 )π r−1

=300πr−π r3

2dvdr =300

2−3 π r2

2 =0

=150- 3π r2

2

3 π r2

2=150

3 π r 2=300π r2=100 r=5.64 cm

h=300−π r2

2 πr

=300−π (5.64)2

2π (5.64)

h=5.64cm