Associated Topics || Dr. Math Home || Search Dr. Math

### Net of a Box

```
Date: 05/23/99 at 14:31:17
From: Holley Goodwin
Subject: Drawing a flat pattern of a box

Hi,

I am a 7th grader, and my teacher asked me to do a project to present
to the class. She asked me to come up with some dimensions (length,
width, and height) and find the surface area and volume. Then I was
told to draw a flat pattern of the box, I don't know how to do any of
```

```
Date: 05/24/99 at 13:11:38
From: Doctor Peterson
Subject: Re: Drawing a flat pattern of a box

Hi, Holley.

Here's an idea for making this an impressive (and helpful) project.

Find some kind of small cubes - maybe baby blocks left over around
your house, or dice, or something like that. Measure them and see how
many you have. Then you can actually show the volume of the box you
make by putting that many blocks inside it; and you can show the area
by pasting the right number of paper squares on the outside of it.

Let's suppose you want to make a box like this, with dimensions in
"blocks" (that is, using the edge of your blocks as a unit of length;
I'll suppose that the blocks are one-inch cubes):

EMPTY BOX

+-------------------+
/                   /|
/                   / |
/                   /  |
+-------------------+   | 4
|                   |   |
|                   |   |
|                   |   |
|                   |   +
|                   |  /
|                   | /
|                   |/ 2
+-------------------+
5

To find the volume, you will have to count the number of blocks you
can fit. If you make one layer on the bottom, it will take 5x2 = 10
blocks:

BOX WITH ONE LAYER OF BLOCKS

+-------------------+
/                   /|
/                   / |
/                   /  |
+-------------------+   | 4
|                   |   |
|   +---+---+---+---+---+
|  /   /   /   /   /|  /|
| +---+---+---+---+-|-+ +
|/   /   /   /   /  |/|/
+---+---+---+---+---+ +
|   |   |   |   |   |/ 2
+---+---+---+---+---+
5

Four layers like this will take 4x16 = 64 blocks:

BOX WITH FOUR LAYERS OF BLOCKS

+---+---+---+---+---+
/   /   /   /   /   /|
+---+---+---+---+---+ +
/   /   /   /   /   /|/|
+---+---+---+---+---+ + + 4
|   |   |   |   |   |/|/|
+---+---+---+---+---+ + +
|   |   |   |   |   |/|/|
+---+---+---+---+---+ + +
|   |   |   |   |   |/|/
+---+---+---+---+---+ +
|   |   |   |   |   |/ 2
+---+---+---+---+---+
5

Now to make a flat pattern, you need to lay out the six sides of the
box so they will fold up. Here's one way:

5
+-------------------+
|                   |
|        top        |2
2   |                   |   2
+-------+-------------------+-------+
|       |                   |       |
|       |                   |       |
|       |                   |       |
| left  |       front       | right |4
|       |                   |       |
|       |                   |       |
|       |                   |       |
+-------+-------------------+-------+
|                   |
|      bottom       |2
|                   |
+-------------------+
|                   |
|                   |
|                   |
|       back        |4
|                   |
|                   |
|                   |
+-------------------+

Now you can find the surface area by adding up the areas of the six
sides, each of which you can find by multiplying its length times its
width.

Even if you don't actually fill it with cubes (which would require
very careful measurements), just thinking of it this way should help
you understand what it's all about.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Euclidean/Plane Geometry
High School Geometry
High School Polyhedra
High School Projects
Middle School Geometry
Middle School Polyhedra
Middle School Two-Dimensional Geometry

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search