Cereal Box
Name __________________________________
Date ____________________________________
Cereal boxes come in different shapes and sizes. Some are tall and skinny, while
others are shorter or deeper. The Bravo Breakfast cereal company is considering
changing the size of its box. The staff members need some data to help them
make the best choice.
The company currently packages its Morning Math
Crunch cereal in a box that
is 2" deep by 4" wide by
8" tall, as pictured at right. This shape is called a
right rectangular prism because the top and bottom faces are rectangles that
are congruent (same size and shape) and parallel to each other. These are called
the bases. The other faces (sides of the box) are also rectangles that are
perpendicular (at a right angle) to the bases. Use a set of cubes to build a model
of this box. Assume that the edge of one cube represents 1" of length on the
Check in the box when you have done this.
real cereal box.
The cardboard sides of the box are called its faces. How much cardboard is
needed to create all six of the faces of the box? Work with your team to develop
a method for calculating this amount. Discuss the kind of units to use. Explain
your method below. Go ahead and calculate the amount of cardboard required.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
The number of square units that it takes to cover the outside of an object, like the
amount of cardboard you found in part (b), is called the object’s surface area.
The volume of a shape is the measure of how much it will hold. Volume is
measured in cubic units. How many cubes did you use to make this model of
the cereal box? How many cubic inches of cereal will the box hold?
_____________
The waste-management division at Bravo Breakfast is worried that the box for
Morning Math Crunch uses too much cardboard. The waste-management crew
wants to make a box that holds the same amount of cereal but uses less
cardboard.
What measurement of the box is the waste-management division interested in
minimizing (making as small as possible)? What measurement does the
company want to keep the same? What could change? __________________
_____________________________________________________________
With your team, use the cubes to build different rectangular prisms that will still
hold 64 cubic inches of cereal. Each box must be a rectangular prism with
exactly six faces. For each prism you create:
---Sketch
---Label
the prism,
the dimensions on your sketch, and
---Find the surface area. How many different prisms can you make? _______
________________________________________________________________
Do all of the prisms you built have the same volume? How do you know?_____
________________________________________________________________ 
Which box will use the smallest amount of cardboard? ____________________
Use cubes to build each prism below. Find the surface area and volume of each
shape.
c. Use at least 15 cubes to build a prism of your own design. Sketch the prism
and find its surface area and volume.