Finding
the right box for a particular product requires a lot of thought
and planning. A company must consider how much a box can hold
and the amount and cost of the material needed to make the box.
The amount
that a box can hold depends on its volume. The volume
of a box is the number of unit cubes that would fill the box.
The amount of material needed to make or cover a box depends
on the box's surface area. The surface area of a box
is the total area of all of its faces.
The box shown below has dimensions 1 centimeter by 3 centimeters
by 1 centimeter. It would take three 1-centimeter cubes to
fill this box, so the box has a volume of 3 cubic centimeters.
Since it takes fourteen 1-centimeter grid squares to make
the box, the box has a surface area of 14 square centimeters.
In this
investigation, you will explore the possible surface areas for
a rectangular box that holds a given amount. In other words,
you will investigate the range of possible surface areas for
boxes with a fixed volume.
