Something as small as a…Hershey’s Kiss??
In recent months, there have been many environmentally-themed commercials on TV. One
such commercial discusses the impact that water bottles have on landfills. According to their data,
the United States discards approximately 30 billion water bottles in a year (66 million per day). If you
consider the average height and weight of a water bottle, how much plastic does that amount to? If
the bottles were stacked on top of each other, could they reach the moon? Would they weigh as
much as a cruise ship? You would be surprised at the answer.
Of course water bottles are larger pieces of discarded items. But what about something smaller…like
a Hershey’s Kiss? Each candy comes in its own foil wrapper. Then, there’s the iconic banner that says
“kisses” on it. You remove the candy from the wrapper, ball it up and throw it away (the wrapper of
course). No thought goes into the tiny discarded piece of aluminum and paper. It’s so small…who
cares? Well…should you?
The purpose of this investigation is to conceptualize how something so miniscule can become
enormous when looked at globally and not individually.
Before you begin, look at some interesting facts about the little candy (source:
http://voices.yahoo.com/):
Fact #1: Hershey's kisses were first produced in 1907. Although no one today seems to know where the
candy got its name, the most popular story says it came from the sound that the machine made as it
deposited the chocolate onto the conveyor belt during the manufacturing process.
Fact #2: Kisses are not made via a mold, but by a special machine that literally drops the chocolate, in a
precise amount, onto a moving belt. They are then cooled quickly to form the now famous "kiss"
shape.
Fact #3: There are more than 80 million kisses made every day at the Hershey plants in Pennsylvania,
California, and Virginia.
Fact #4: The kiss turned 100 years old on July 7, 2007 with the unveiling of the world's largest kiss in
Hershey, Pennsylvania. It weighed 30,540 pounds.
Created by Chris Fletcher, Cheshire High School, Cheshire CT, cfletcher@cheshire.k12.ct.us
Page 1
1. Randomly select 10 candies from the bag provided by the teacher. Carefully unwrap the candies
and set everything aside (try not to rip the foil wrapper or break the chocolate). Using the
measuring tools provided, fill in the table below.
Sample
Dimensions
(L x W) of foil
wrapper
(in cm)
Weight of foil (in
grams)
Length of paper
banner (in cm)
Weight of paper
banner (in grams)
Weight of
chocolate
(in grams)
1
2
3
4
5
6
7
8
9
10
Mean (if
applicable)
Standard
Deviation (if
applicable)
Created by Chris Fletcher, Cheshire High School, Cheshire CT, cfletcher@cheshire.k12.ct.us
Page 2
2. Based on the results from the previous page, what would you determine to be the characteristics
of the “typical” kiss (including the wrapper and banner)? Your answer may be a single number, or an
interval of numbers. Justify your choices
Dimensions (L x W) of
foil wrapper (in cm)
Weight of foil (in
grams)
Length of paper
banner (in cm)
Weight of paper
banner (in grams)
Created by Chris Fletcher, Cheshire High School, Cheshire CT, cfletcher@cheshire.k12.ct.us
Weight of chocolate
(in grams)
Page 3
3. Revisit your 10 chocolate kisses. You recorded the weights, but you found tiny variations in those
numbers. Although there are strict quality control measures in manufacturing, it is expected that not
every candy will be exactly the same. Accurately measure the diameter and height, and fill in the
table below.
Sample
Diameter of base (in cm)
Height (in cm)
1
2
3
4
5
6
7
8
9
10
Mean (if applicable)
Standard Deviation (if applicable)
Created by Chris Fletcher, Cheshire High School, Cheshire CT, cfletcher@cheshire.k12.ct.us
Page 4
4. Now that you know the dimensions of your 10 kisses, what is the volume of chocolate for those
candies? Perhaps the volume of chocolate is the quality control Hershey strives for…not the
dimensions. Can you determine the volume of the kiss by using a geometric formula? Could you
apply the concept of volume by revolution around an axis? Could you use definite integrals from
Calculus? Choose a method (or two) and determine the volume. Pay careful attention to the units.
WORK
Sample
Volume (cm3)
1
2
3
4
5
6
7
8
9
10
Mean (if applicable)
Standard Deviation (if
applicable)
Created by Chris Fletcher, Cheshire High School, Cheshire CT, cfletcher@cheshire.k12.ct.us
Page 5
5. Are your calculations from the last question correct? We’ll let science decide. If you modify a
popular science formula: 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 =
𝑚𝑎𝑠𝑠
𝑣𝑜𝑙𝑢𝑚𝑒
to be 𝑽𝒐𝒍𝒖𝒎𝒆 =
𝒎𝒂𝒔𝒔
𝒅𝒆𝒏𝒔𝒊𝒕𝒚
you could determine the
volume. But, in order to do this, you need to know the density of Hershey’s chocolate.
Hmmmm…..time to do some research to find out what the density of Hershey’s chocolate is. Pay
careful attention to the units.
Sample
Weight (mass) of chocolate
(in grams)
Density of Hershey’s
chocolate
𝒎𝒂𝒔𝒔
Volume = 𝒅𝒆𝒏𝒔𝒊𝒕𝒚
1
2
3
4
5
6
7
8
9
10
Mean (if applicable)
Standard Deviation (if
applicable)
Created by Chris Fletcher, Cheshire High School, Cheshire CT, cfletcher@cheshire.k12.ct.us
Page 6
6. Compare the volume you calculated in question #4 to the volume in #5.
Sample
Volume
(from #4)
Volume
(from #5)
Difference
1
2
3
4
5
6
7
8
9
10
Mean (if applicable)
Standard Deviation (if
applicable)
Created by Chris Fletcher, Cheshire High School, Cheshire CT, cfletcher@cheshire.k12.ct.us
Page 7
7. So which is it? Do you think the quality control is in the volume of chocolate, or the size of the
kisses, or both? Justify your choice.
Created by Chris Fletcher, Cheshire High School, Cheshire CT, cfletcher@cheshire.k12.ct.us
Page 8
8. According to data found on the internet (always be careful with data from the internet), 80 million
kisses are produced per day. With this number in mind, and assuming a 5 day work week of 8 hours
per day, fill in the table below:
How many kisses are
produced?
Weight of foil
wrappers (in grams)?
Length of banners (in
cm)?
Weight of chocolates
(in grams)?
per second?
per minute?
per hour?
per week?
per year?
per decade?
per century?
If necessary, write answers in scientific notation!
WORK
Created by Chris Fletcher, Cheshire High School, Cheshire CT, cfletcher@cheshire.k12.ct.us
Page 9
9. Assuming a constant rate of production, how long would it take Hershey to produce a banner that
would accomplish the following (write answer in most appropriate unit of time-days, months, years).
Then, calculate the weight of such a banner.
How long?
Weight of paper (in pounds)
stretch from NYC to LA?
stretch from NYC to Tokyo?
circle the Earth?
reach the moon?
reach the sun?
Created by Chris Fletcher, Cheshire High School, Cheshire CT, cfletcher@cheshire.k12.ct.us
Page 10
10. Assuming a constant rate of production, how long would it take Hershey to produce enough foil
wrappers to cover (write answer in most appropriate unit of time):
How long?
A standard football field?
the city of Hartford?
the state of CT?
the United States?
the Earth?
Created by Chris Fletcher, Cheshire High School, Cheshire CT, cfletcher@cheshire.k12.ct.us
Page 11
11. Refer to question #10. Imagine taking the wrappers and turning them into a solid block of
aluminum. How big would the cube be and how much would it weigh? Since aluminum foil has a
density of 2720 kg/m3, we can use this number to help us determine the size of the resulting cube.
How big is the cube for each scenario above and how much would it weigh?
Weight of foil (in kg)
Weight of foil (in
pounds)
Size of aluminum cube
(m x m x m)
Size of aluminum cube
(ft x ft x ft)
A standard football
field?
The city of Hartford?
The state of CT?
The United States?
The Earth?
Created by Chris Fletcher, Cheshire High School, Cheshire CT, cfletcher@cheshire.k12.ct.us
Page 12
12. What should Hershey do about addressing the excessive use of materials? Should they eliminate
the foil wrappers? What would be reasons to support this? What would reasons be in opposition to
this?
Created by Chris Fletcher, Cheshire High School, Cheshire CT, cfletcher@cheshire.k12.ct.us
Page 13
13. Rather than eliminating the wrapper, what if Hershey considered redesigning it? For the last part
of the assignment, design your own wrapper that could accomplish the same job, but save the
company money in wasted materials (and make them more environmentally friendly). You can
experiment with aluminum foil (or other materials) to devise an alternative. When you settle on an
alternative design, demonstrate the details of the new wrapper (both a physical model and a diagram)
and write a letter to Hershey explaining how much money it will save the company, how it will be
equally effective in covering the chocolates, how it will be more environmentally friendly, etc…
Opening scene to Willy Wonka and the Chocolate Factory
http://www.youtube.com/watch?v=OrhBZwmEK8I
Youtube video describing how to find the density of a Hershey’s chocolate bar
http://www.youtube.com/watch?v=FOemgz251hI
To view more amazing statistics regarding recycling and environmental impacts, visit:
http://www.cleanair.org/Waste/wasteFacts.html
Created by Chris Fletcher, Cheshire High School, Cheshire CT, cfletcher@cheshire.k12.ct.us
Page 14