Net of a BoxDate: 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 that. Can you please help me? 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/ |
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