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### Dimensions of a Cardboard Box

```
Date: 09/28/97 at 14:37:01
From: Steve

A box with a square bottom and a volume of 2000 centimeters can be
made by cutting 5-centimeter squares from the corners of a piece of
cardboard and then turning up the sides.

What should be the dimensions of the piece of cardboard?

```

```
Date: 10/22/97 at 11:14:04
From: Doctor Mandel
Subject: Re: 9th grade Math.....Brain Twister

Dear Steve,

You know that the sides of the box must be 5 cm high because the
pieces you cut out of the flat board are 5 cm squares, so the walls
are 5 cm tall. The volume of a box is equal to the area of the base
times the height.  Since you know the height and the volume of the box
you can find out the area of the base. Just write out the equation:

volume = (area of base)(height)

and plug in a numbers you already know.

Since you know that the base is a square you can find the length of
one side of the base by finding the square root of the base's area.
The length of the original side is the length of the base plus 10 cm,
five on each side.

Here's what the unfolded box would look like:

|-5 CM--|--SIDE OF BOX--|-5 CM--|
-------------------------------  -
|XXXXXXX|               |XXXXXXX| |
|CUT OUT|               |XXXXXXX| 5 CM
|XXXXXXX|               |XXXXXXX| |
|-------|----FOLDS------|-------| -
|       |               |       |
|       |               |       |
|       |               |       |
|       |               |       |
|       |               |       |
|       |               |       |
|       |               |       |
|-------|---------------|-------|
|XXXXXXX|               |XXXXXXX|
|XXXXXXX|               |XXXXXXX|
|XXXXXXX|               |XXXXXXX|
-------------------------------

-Doctor Mandel,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Geometry
High School Higher-Dimensional Geometry
High School Polyhedra
Middle School Geometry
Middle School Higher-Dimensional Geometry
Middle School Polyhedra

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