Do you know what “volume” means? It means how much stuff an object can hold inside it. We’re going to make a couple of cylinders (a rolled-up tube) from a piece of paper and compare how many styrofoam pellets it can hold. The question is, “Will a tube made from a piece of paper have a different volume if you roll it from its width versus its length?”
Will it make a difference which way you roll it up or will the volume be the same because it’s the same piece of paper? Let’s proceed and find an answer!
Materials:
- Two sheets of paper, preferably 8 ½” x 11”
- Tape
- Styrofoam packing pellets
Procedure:
- Roll a piece of paper widthwise to make a short, wide tube. Don’t overlap the edges and tape it together
- Roll another same-sized piece of paper the other way to make a long and narrow tube. Tape it together
- Fill each cylinder with packing pellets all the way to the top
- Dump out each tube and count them to see which has more!
Explanation:
You should have been able to fit more pellets in the one that wasn’t as tall. Not a lot more, but definitely more. Why is that? It seems weird, right? It’s the same piece of paper, shouldn’t you have the same amount of volume no matter which way you roll it?
But no, it doesn’t work out that way. There’s a mathematical explanation as to why, and I’ll try to make it simple, although it probably won’t be. The volume is dependent upon a couple of factors, one of which is the radius, or half of the distance across the round top portion. When calculating volume, you have to do some math which makes the radius have a bigger impact on the results. The wider portion has a bigger radius, which makes the volume come out bigger than the other.
Going further:
Will this work with different shapes? Like if you try to make a cone with different sides of the piece of paper? Try out some of your own ideas to test! This is a tricky thing to understand mathematically, but if you grasp the concept you’ll have a good geometric ability.
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About the author:
Steve Davala has been teaching math and science to middle and high schoolers since 2000. He writes books, plays music, carves wood and he loves learning new things. Ask him a question at steve.davala@gmail.com.
