Add Maths Project 2012

Popcorn

Popcorn is a type of corn that expands from the kernel and puffs up when heated. Corn 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. This allows pressure to build inside the kernel until an explosive "pop"

results. Some strains of corn are now cultivated specifically as popping corns. The kernels are sometimes different than others.

There are many techniques for popping corn. Commercial large-scale popcorn machines were invented by Charles Cretors in the late 19th century. Many types of small-scale home methods for

popping corn also exist, with the most popular in the United States being pre-packaged.

Depending on how it is prepared and cooked, some consider it 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…

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 colour.

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.

Section A

1.

2. The two cylinders will not hold the same amount. One of the

cylinders will hold a bigger volume than the other which is

the cylinder with the larger radius. This is because volume of

the cylinder is more influenced by the radius than the

diameter of the cylinder.

4. a) My prediction was correct; Cylinder B could contain

more popcorn than Cylinder A. This is proven when

there is still more empty space to fill in more popcorn

in Cylinder B

b) IGNORED

5. a) Having a right circular cylinder with a height h units

and a base of radius r units with the coordinate axes

chosen so that the origin is at the centre of one base

and the height is measured along the positive x-axis.

A plane section at a distance of x units from the

origin has an area of square units where:

DIMENSION CYLINDER A CYLINDER B HEIGHT 12 8.6

DIAMETER 2.8 3.4 RADIUS 1.4 1.7

An element of volume, is a right cylinder of base

area square units and a thickness of units.

Thus if V cubic units is the volume of the right circular

cylinder, by *Riemann sums:

∑

∫

∫

And by using cylindrical coordinates, the volume can

also be calculated by integration over:

∫ ∫ ∫

b) Volume of Cylinder A:

(12)

c) Volume of Cylinder B:

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

6. Volume is determined by using formula,

Original;

RADIUS HEIGHT VOLUME 3 10 282.74

Increased Radius;

RADIUS HEIGHT VOLUME 4 10 502.65 5 10 785.40 6 10 1130.97 7 10 1539.38 8 10 2010.62

Increased Height;

RADIUS HEIGHT VOLUME 3 11 311.02 3 12 339.29 3 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

Section B

Hint: 300cm2 of thin sheet material is given

Objective: Container that can contain the most popcorn

Container to contain the MOST VOLUME for its surface area.

Different shapes (OPEN TOP) to be used;

Cube

Cuboid

Cylinder

Cone

Hemisphere

Cube;

l

l

l

Hemisphere;

r

h

Cuboid;

(

)

l

l

h

l

Cylinder;

(

)

h

r

Cone;

√

(

)

(

)

r

h

Tabulation

Hence, 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 more bang

for my buck!!!

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 profits

ii. If I was the producer of the containers, I would choose the

CONE container can contain much popcorn at the same time,

saves the manufacturing costs

CONTAINER HEIGHT RADIUS LENGTH WIDTH VOLUME CUBE 7.7460

cm X 7.7460

cm 7.7460

cm 464.76

cm3 HEMISPHERE X 6.9090

cm X X 690.99

cm3 CUBOID 5 cm X 10 cm 10 cm 500.00

cm3 CYCLINDER 5.6419

cm 5.6419

cm X X 564.19

cm3 CONE 10.5006

cm 7.4252

cm X X 606.03

cm3

Conclusion

From this project, I have learned to determine the volume of

containers of different shapes. And I have also learned that in a

cylinder container, the radius of the cylinder container increases

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 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 be manufactured 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.

Table of Contents

No. Title Page

1 Front Cover

2 About Me

3 Table of Contents

4 About Popcorn

5 History of Popcorn

6 Section A

7 Section B

8 Tabulation

9 Conclusion

10 Credits

About Me

NAME : MUHAMMAD AKMAL HAKIM

CLASS : 5 SC. ALPHA

SUBJECT CODE :

I/C NUMBER : 950329-14-5803

TEACHER : PN. ZURAIMAH