ADDITIONAL MATHEMATICSPROJECT WORK(TASK 2)SIJIL PELAJARAN MALAYSIA 2014SMK BUKIT JALIL

Name: Class: Team Members: Teachers Name:

NOCONTENTPAGE

1ACKNOWLEDGEMENT1

2OBJECTIVE2

3INTRODUCTON History of Popcorns History of Polygons3

4SECTION A Question 1 Question 2 (a) (b) Question 3 Question 4 (a) (b) Question 5 (a) (b) (c) (d) Question 6

5

5SECTION B Container 1 Container 2 Container 3 Container 4 Container 5 Container 610

6CONCLUSION17

7REFLECTION19

ACKNOWLEDGMENT First and foremost, I would like to thank God that finally, I have succeeded in finishing this project work. I would like to thank my beloved Additional Mathematics, ________ for all the guidance she had provided me during the process in finishing this project work. I also appreciate her patience in guiding me completing this project work.

Second, I would like to give a thousand thanks to my parents for giving me their full support in this project, financially and mentally. They gave me moral when I needed it. Who am I without their love and support? I would also like to give my thanks to my fellow friends who had helped me in finding the information that Im clueless of, and the time we spent together in study groups on finishing this project work.

Last but not least, I would like to express my highest gratitude to all those who gave me the possibility to complete this coursework. I really appreciate all the help I got. Again, thank you very much.

OBJECTIVE

I. Apply and adapt avariety of problem-solving strategies to solve routine and non-routine problems.

II. Acquire effective mathematical communication through oral and writing, and touse the language of mathematics to express mathematical ideas correctly and precisely.

III. Increase interest andconfidence as well as enhance acquisition ofmathematical knowledge and skills that are usefulfor career and future under takings.

IV. Realize that mathematics is animportant and powerful tool in solving real-life problems and hence develop positive attitude towards mathematics.

V. Train students not only tobe independent learners but also collaborate, to cooperate, and to share knowledge in anengaging and healthy environment.

VI. Use technology especially the ICTappropriately and effectively.

VII. Train students to appreciate the intrinsic valuesof mathematics and to become more creative and innovative.

VIII. Realize the importance and the beauty ofmathematics.

INTRODUCTIONI. History of PopcornsPopcorn was first discovered thousands of years agoby Americans. It is one of the oldest forms of corn: evidence of popcorn from 3600 B.C. was found inNew 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 510 cents a bag and became popular. Thus, while other businessesfailed, 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 timesas 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 thispurpose; 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 snackfood ofIllinois, U.S.A.

II. History of Polygons

A polygon is a flat shape consisting of straight lines that are joined to form a closed chain or circuit.

A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments (i.e., by a closed polygon chains). These segments are called its edges or sides, and the points where two edges meet are the polygons vertices (singular: vertex) or corners. An n-gon is a polygon with n sides. The interior of the polygons is sometimes called its body. A polygon is a 2-Dimensional example of the more general polytope in any number of dimensions.

The word polygons derives from the Greek (pols) "much", "many" and (gna) "corner" or "angle". (The world gnu with a short o, is unrelated and means "knee".) Today a polygon is more usually understood in items of sides.

The basic geometrical notion has been adapted in various ways to suit particular purposes. Mathematicians are often concerned only with the bounding closed polygonal chain and withsimple polygonswhich do not self-intersect, and may defined a polygon accordingly. Geometrically two edges meeting at a corner are required to form an angle that is not straight (180); otherwise, the line segments may be considered parts of a single edge; however mathematically, such corners may sometimes be allowed. In fields relating to computation, the term polygon has taken on a slightly altered meaning derived from the way the shape is stored and manipulated in computer graphics (image generation).

Polygons have been known since ancient times. The regular polygons were known to the ancient Greeks, and the pentagram, a non-convex regular polygons (star polygon), appears on the vase of Aristophonus, Caere, dated to the 7th century B.C. Non-convex polygons in general were not systematically studied until the 14th century by Thomas Bredwardine. In 1952, Shephard generalized the idea of polygons to the complex plane, where each real dimension is accompanied by an imaginary one, to create complex polygons.

SECTION A

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

Take the colored paper and roll it up along the shorter side to from 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 your data below and on the cylinder. Label it as Cylinder B.

DIMENSIONCYLINDER ACYLINDER B

Height11.08.5

Diameter2.63.4

Radius1.31.7

2. (a) Do you think the two cylinders will hold the same amount? The two cylinders will hold the different amount.

(b) Do you think one will hold more than the other? Which one? Why? Cylinder B will hold more than Cylinder B. Because the radius of Cylinder B is longer and this make the volume is bigger that Cylinder A. Although the height of Cylinder B is shorter than Cylinder A, but this does not affect much compare the affect of different in radius.

3. Place cylinder B on the paper plate with Cylinder A inside it. Use your cup to pour popcorn into Cylinder A until it is full. Carefully, lift Cylinder A so that the popcorn fall into Cylinder B. Describe what happened. Is Cylinder B full, not full, or overflowing?1. Cylinder B is not full. There is still space in the Cylinder B for more popcorn after Cylinder A had been lifted up.

4. (a) Was your prediction correct? How do you know?2. Yes, the prediction is correct. It is based on the formula, volume of cylinder equals to rh. Thus, the Cylinder B with greater radius, r have the greater volume, V than Cylinder A.

(b) If your prediction was incorrect, describe what actually happened.3. Cylinder B has a greater volume than Cylinder A.

5. (a) State the formula for finding the volume if a cylinder.4. V= rh

(b) Calculate the volume if Cylinder A?

5. V = rh = x 1.3 x 11 = 58.4 inch

(c) Calculate the volume of Cylinder B?

6. V = rh = x 1.7 x 8.5 = 77.2 inch

(d) Explain why the cylinders do or not hold the same amount. Use the formula for the volume of a cylinder to guide your explanation.7. The cylinders have different radius and heights, so the volumes are different.

Data and Observations:I. The cylinder with have the greater radius and diameter will have the greater volume.II. The radius of Cylinder B is greater than Cylinder A.III. The volume of Cylinder B is greater than Cylinder A.IV. So, Cylinder B holds more popcorn than Cylinder B.

DIMENSIONCYLINDER ACYLINDER B

Height, inch11.08.5

Diameter, inch2.63.4

Radius, inch1.31.7

Volume, inch58.477.2

1. 2. 3. 4. 5. 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.

CYLINDERRADIUSHEIGHTVOLUME

Original310

Increased Radius

Increased Height

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

CYLINDERRADIUSHEIGHTVOLUME

Original310282.7

Increased Radius410502.7

Increased Height311311

8.

Increasing the radius increased the volume more than increasing the height. This is because the radius squared to find the volume, which increases its impact on the volume.

SECTION A

If 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 cm of thin sheet material. Explain the details.

1. Cylinder Container- (Opened Up)

Surface Area = 2rh + r = 300h = Volume = rh = r ( ) Maximum Volume = = 0r ( ) = ( ) = ( )= = = 150 -

= 150 3r = 300 r = 100 r = 5.64 cm

Volume = 563.62 cm

h = = h = 5.64 cm

2. Cube container- (Opened Up)

Surface Area = l + 4l = 300 cm 5l = 300 l = 60l = 7.75 cm

Volume = l = (7.75) = 465.48 cm

3. Cuboid Container- (Opened Up)

- Assume that length is twice its width or others

Surface Area = 2l + 4hl = 300 cmh = Volume = 2lh= 2l ( )Maximum Volume = = 0 2l ( ) = ( )= ( )= 1501 - l= 150 3l = 0

150 = 3l l = 50 l = 7.07 cm

h = = 7.07 cm

Volume = 2lh= 2(7.07)(7.07)= 706.79 cm

4. Cuboid Container- (Opened Up)

- Assume that length is equal to its width

Surface Area = l + 4hl = 300h = Volume = lh = l ( )Maximum Volume = = 0 = 75 - = 0 75 =

l = 10 h = 5

Volume = 500 cm

5. Hexagon Container- (Opened Up)

- Assume that the of the side = x

Area of the base = 6 = 6 = xhSurface Area = 6hx + ( x) = 300h = Volume = base area x height = xh = x()Maximum Volume = = 0= - = x = 4.39h = 9.49Volume = 475.17 cm6. Cone Container- (Opened Up)

- From the diagram, x = r + h

Surface Area = r x = 300 cmrx = 300 r (r + h) = 90000 h = Volume = rhVolume = h = ()Maximum Volume = = 0 = 1000 - = 0 = r = 7.42h = 10.51Volume = (7.42) (10.51) = 605.95 cm

CONCLUSIONCONTAINERHEIGHTRADIUSLENGTHWIDTHVOLUME

Cylinder5.64---563.69

Cube7.75-7.757.75465.48

Cuboid 17.07-7.0714.14706.79

Cuboid 25.00-10.0010.00500.00

Hexagon9.49-4.39 (side)-475.17

Cone10.517.42--605.95

Shapes 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 cuboid1 can be filled in with the most amount popcorn. It followed by cone, cuboid 2, and 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 cuboids shapes can be found. Therefore, in this case, the cuboid1 was the most preferable container that can have the most popcorn.

I. You are the popcorns sellers, 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 the easiest production and it takes less effort and also no time consuming to produce.

REFLECTIONWhile I concluding this project, a lot of information that I found. I have learnt the uses of polygons. I also learned some moral values that I practice. This project had taught me to be responsible on the works that are given to me to be completed. This project also made me felt more confidence to do works and not to give up easily when we could not find the solution for the question. I also learned to be more discipline ob time, which I was given about three weeks to complete these project and pass up to my teacher just in time. I also enjoyed doing this project during my school holiday as I spent my time with friends to complete this project and it had tightened our friendship.