How many pieces of popcorn will fit in the Rye Neck Dining Hall? How long
would it take a 12 year old boy to eat all of the popcorn?
When we first received this essay I honestly thought that you were insane.
Then as I
thought about it some more I realized that it wouldn’t be SO bad. I also realized that I would
need to find the volume of the Dining Hall to figure out how many pieces of popcorn would fit
inside of it. The first thing I did, that is after I got the Dining Hall measurements, was try to
break it down into sections. I couldn’t just do one big measurement for a few reasons. One
reason was because the height of the dining hall changes in several different places. Another
reason was because there is a curve in the dining hall, which changes the shape. Thirdly because
it is an irregular shape making it so that you cant use the simple formula of length times width
times height. Because of these things, I broke the Dining Hall into 9 sections.
After I broke the Dining Hall into sections, I made sure that all of me measurements were
in feet. Since there were many measurements that were still in inches I converted them into feet
by diving each one by 12. I divided them by 12 because there are 12 inches in one foot.
Now that my measurements were all in inches it was time to start finding the volume of
each section. To find the volume of sections 1, 2, 3, 4, 5, 8 and 9 I did length x width x height
(as shown in the diagram). Because of the shape of sections 6 and 7, I had to add a few
additional steps before using length x width x height. Because section 6 was where the curve
began, I used the measurement in the diagram that showed each section was 11 feet 1 inch (refer
to diagrams). Then because of the curve, the width of section 6 was not the same on both sides.
So I decided to find the average of the two widths and use the answer as the width in my
equation. Then, I broke section 7 into a triangle and a rectangle because the curve was still
active here. I looked on the building plan pictures that Whitney sent us, to find out that the base
of the triangle was 4 ft. Then I found the volume of the triangle (as if it were a rectangle) and
divided it by two to find its volume. Then I found the volume of the rectangle that made up the
remaining part of section 7. Lastly, I added the two volumes together to find the volume of all of
section 7.
Once I found the volumes of the different sections, I then added them all together to find
the total volume of the dining hall. I added 7612.81 ft³ (sect. 1) + 184 ft³ (sect. 2) + 12382.28 ft³
(sect. 3) + 1700 ft³ (sect. 4) + 44497.84 ft³ (sect. 5 and 6) +4153.185 ft³ (sect. 7) + 7590 ft³
(sect.8) + 14086.695 ft³ (sect. 9) = 92206.8 ft³ ( total volume of the Dining Hall).
Now that I had found the total volume of the Dining Hall it was time to find out the
volume of the columns, condiment counter, cashier area, etc. But luckily you told us that we just
need to find the volume of the skeletal structure of the Dining Hall. This saved me a lot of work.
Now that half of the question was complete, it was time to work on completing the other
half of our problem. I decided to email me cousin Thomas and ask him if he would like to be a
part of my math project. He agreed and I told he and my aunt what I needed them to do. I asked
the to find out how long it would take Thomas to eat 10 pieces of popcorn and then to find out
how many pieces of popcorn he could eat in one minute.
When they finished the test/
experiment they emailed me the results. The results showed that it took Thomas 52 seconds to
eat 10 pieces of popcorn and that it took him one minute to eat 20 pieces of popcorn. With the
test results in hand, it was time to do some crazy calculations.
The first thing I did was try to find out how many pieces of popcorn would fit in the
Dining Hall. My dad suggested that I make a 6 x 6 x 6 in cube, fill it with popcorn, and then
figure out how many cubes would fit in the dining hall. So I made the cube and began to fill it.
After putting about 20 pieces of popcorn in the cube, I looked in and saw that I hadn’t nearly
even covered the bottom of the cube. So I decided to change and make a 1 x 1 x 1 in cube. This
cube held 3 pieces. I started thinking about that and how many of the 1 x 1 x 1 cubes I would
need to fill the Dining Hall and then decided to go back to my 6 x 6 x 6 cube. I just dumped the
popcorn in until it was full to the top. Once it was full, made dad and I began to count. Every
time one of us reached 20 pieces we would write it down on the piece of paper and then we
added all the 20’s up at the end. We found that there were 870 pieces of popcorn in on 6 x 6 x 6
in cube.
The next step was to find out how many 6 x 6 x 6 in cubes were in one 12 x 12 x 12 in
cube. After careful thought and almost making a mental model, we found that there were eight,
6 x 6 x 6 in cubes in one 12 x 12 x 12 in cube. So I multiplied 870 by 6 to get 6960 pieces. This
means that there are 6960 pieces of popcorn in one foot³.
Now it was time to figure out how many pieces of popcorn fit into the Dining Hall and
how long it would take Thomas to eat all of the popcorn. To find out how many pieces were in
the Dining Hall I multiplied 99206.81 (the volume of the Dining Hall) by 6960 (the amount of
pieces in one foot³) and got 641,759,397.6 pieces. Since I knew that my cousin could eat 20
pieces of popcorn in one minute, I multiplied 20 by 60 to find out how many pieces he could eat
in one hour, to find that he can eat 1200 pieces in one hour. Then I did 1200 x 24 = 28800 which
told me the number of pieces he could eat in a day. Lastly, I did 28800 x 365 = 10512000, which
told me that Thomas could eat 10,512,000 pieces of popcorn in one year. Finally, I divided the
number of pieces of popcorn that could fit in the Dining Hall (641,759,397.6) by the number of
pieces of popcorn that Thomas could eat in a year (10512000) to get 61.05 years. So, if would
take Thomas 61.05 years to eat all the popcorn in the cafeteria if he eat non stop.
Though, the way that I approached and solved this problem is logical, there are many
mistakes that could have been made. For example, I could have miscalculated when I transfered
the inches into feet, which would result in a change in the total volume. Another error that could
have occurred, is that the 6 x 6 x 6 inch box that I made may not have been exactly 6 x 6 x 6
inches. This would cause the amount of popcorn and the amount of time it would take Thomas
to eat the popcorn to fluctuate. Lastly, a possible error that could have occurred was if the
measurements in the diagram that Whitney gave us were incorrect. This would have messed up
our entire answer. So, with the measurements I was given and my calculations that I developed,
I found that 641,759,397.6 pieces of popcorn would fit in the Rye Neck Dining Hall and that it
would take my cousin Thomas 61.05 years to eat all the popcorn if he ate non stop.
Sources:
-Whitney and Patrick
-Dining Hall Building Plans
-Thomas Laird
-Daddy