Name
Class
Date
Chapter 11 Project: The Place Is Packed
Beginning the Chapter Project
Walk into any supermarket, and look at the shapes lining the shelves. Bottles
of ketchup are tapered like cones. Boxes of cereal stand tall and wide, but
not too deep. Cylindrical cans of tuna are short and wide. Manufacturers
consider dozens of factors before determining which shape will best suit the
consumer and boost the company’s profits.
All rights reserved.
In this chapter project, you will explore package design and uncover some
of the reasons for the shapes that manufacturers have chosen. You also will
design and construct your own package and shipping container. You will see
how spatial sense and business go hand in hand to determine the shapes of
things you use every day.
Activities
Activity 1: Measuring
Collect some empty cardboard containers shaped like prisms and cylinders.
•
Measure each container, and calculate its surface area.
•
Flatten each container by carefully separating the places where it has
been glued together. Find the total area of the packaging material used.
•
For each container, find the percent by which the area of the packaging
material exceeds the surface area of the container.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
1. How does an unfolded and flattened prism-shaped package differ
from a net for a prism?
2. Compare the percents you calculated. What did you find out about
the amount of extra material needed for prism-shaped containers?
For cylindrical containers?
3. Why would a manufacturer be concerned about the surface area of
a package? About the amount of material used to make the package?
Activity 2: Analyzing
Copy and complete the table below for four different rectangular prisms,
each of which has a volume of 216 cm3.
Length
(cm)
Width
(cm)
6
6
Depth
(cm)
Volume (V)
(cm3)
Surface Area (S.A.)
(cm2)
Ratio
V : S.A.
216
216
1. Which of the prisms uses the container material most efficiently? Least
efficiently? Explain.
2. Why would a manufacturer be concerned about the ratio of volume to
surface area?
3. Why are cereal boxes not shaped to give the greatest ratio of volume to
surface area?
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Project
Geometry Chapter 11
Name
Chapter 11 Project
Class
Date
(continued)
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
All rights reserved.
Activity 3: Investigating
Do some container shapes seem to contain more product for the same
money? Go to a supermarket, and identify a variety of container shapes.
Do some shapes make you think that the containers hold more than they
actually do? What factors does a manufacturer consider in deciding the
shape of a container? Write a report about your findings.
Activity 4: Creating
Design and construct your own package for a product of your choice. Draw
a net for your package, and specify the dimensions, surface area, amount and
type of packaging material used, and volume of the package. Justify your
design with mathematical and economic arguments.
Finishing the Project
To ship your product, the individual packages must be packed into larger
containers. Design and build a container that will efficiently pack the
containers you designed in Activity 4: Creating. Draw a net for your shipping container, including dimensions, surface area, the amount and type
of material used, volume of the container, and the number of individual
packages that will be packed in the container. Justify your design with
mathematical and economic arguments.
Reflect and Revise
Ask a classmate to review your project with you. Together, check that
your package design and shipping container are complete, your diagrams
and explanations clear, and your information accurate. Have you used
geometric terms correctly? Have you considered other possible designs?
Revise your work as needed.
Extending the Project
Find pictures of packaged products in newspapers or magazine
advertisements. Identify the shape of each package. Give possible
reasons that the manufacturer chose each package design.
Visit PHSchool.com for information
and links you might find helpful as
you complete your project.
Geometry Chapter 11
Project
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