# Cross-Sections and Nets

## Cross-sections are intersections of a plane with a solid, and nets are unfolded, flat representations of the sides of a 3-D shape.

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Hold the Mail!

Credit: Robert Lopez and Steve Terrebonne
Source: CK-12 Foundation
License: CC BY-NC 3.0

The U.S. Postal Service (USPS) ships 160,000,000,000 pieces of mail every year. The new Priority Mail service is an innovation, and it utilizes nets!

#### News You Can Use

This story is easiest told in pictures. Here is the box in its two-dimensional form, as the USPS prints it. It is cut in several places and pre-folded in such a way that allows it to be constructed into a completely enclosed, weather-proof box.

Credit: Robert Lopez and Steve Terrebonne
Source: CK-12 Foundation
License: CC BY-NC 3.0

You can see that there are two large rectangles that form the top and bottom, and four more that form the sides. Then there are four squares that fold inside the sides as it is assembled, which close the corners.

On the sides we have flaps that fold over to close the top, and the top has “ears” to fit into the slots. Here is the box partly assembled.

Credit: Robert Lopez and Steve Terrebonne
Source: CK-12 Foundation
License: CC BY-NC 3.0

All the major parts of the net are now folded. On the top, you can see a piece of white tape that covers the only adhesive on the whole box; the whole construction is held together by the way it folds and inserts and by this one strip of adhesive.

Credit: Robert Lopez and Steve Terrebonne
Source: CK-12 Foundation
License: CC BY-NC 3.0

This is a simple product, but making it so that it could be easily assembled and safely used took clever design! The whole box takes a package that has the dimensions \begin{align*}5.375 \times 8.625 \times 1.625 \end{align*} inches.

You can find information about the other volumes carried by the USPS here: http://about.usps.com/who-we-are/postal-facts/

#### Explore More

The box in the images above is the smallest Priority Mail package. They are available at U.S. Post Offices if you would like to construct your own box or experiment with different sizes.

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