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Volume of a Cylinder

Volume of a Cylinder
A cylinder is a three-dimensional shape circular in cross section. Cylinders are very common, from cans to tubes, to internal combustion engines. This instructable will show you how to calculate the volume of a cylinder.

What you may not know is that you probably already know how to do this; the instructable will extend the instruction to show how calculating the volume of a cylinder is similar to calculating the volume of other shapes.

This instructable is part of the Burning Questions Round 6.5 contest... If you like this, please vote for me!
 
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Step 1Gather equipment

Gather equipment
You'll need to be able to measure the cylinder. A digital caliper is a good purchase if you're going to be measuring a lot, and there are adequate units for under $30. If you need to measure internal dimensions, then a caliper is the way to go. You'll need:

1. Some type of measuring device
2. A calculator (some units have a dedicated pi key, which would be handy)
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21 comments
Aug 6, 2009. 7:09 PMAmnesia Wes says:
(removed by author or community request)
Aug 7, 2009. 4:55 PMAmnesia Wes says:
Without doing all the calculations: take a tub, fill it to the top with water. Put your cylinder into the water. Take the amount of water that overflows from the tub; pour it into a measuring cup. The measuring cup will then tell you exactly how much volume the cylinder is. Archimedes did this eons ago, screaming Eureka! remember? One of the things I forgot to mention is that this method can be used to determine the volume of any kind of object, whether it's a ball, a cylinder, a cone, etc. In fact, it can even be used to determine the volume of irregular shapes, for example: ask a mathematician to determine the volume of a bowling pin. It'll take him quite some time because of all the curves and dimensions, whereas with this method it will only take mere minutes.
Jul 10, 2011. 7:39 AMCooldeal says:
What about the thickness of the walls of the cylinder? What if the walls were only thick on some of the sides?
Jul 10, 2011. 6:05 PMCooldeal says:
No. Just charge me for the beer I drink out of it instead of the whole volume. Too much computing for me to handle. But I can always fill it then measure what comes out of it.
Feb 25, 2009. 7:49 AMariberman says:
Good overview. Now, can you show me how to do partial volume calculations in a horizontal cylinder? This seems a lot more tricky.
Jun 20, 2011. 9:06 AMespdp2 says:
This can finally lead me to the answer to a real puzzler that was posed on Car Talk on NPR a few months back! A caller had a big-rig with the horizontal (approximately) cylindrical fuel tanks. His gas gauge was on the fritz, and he wanted to know how to tell how much fuel he had. 1/2 tank is easy enough. 1/4 tank or 10% had Ray and Tom stumped, and they put out a request for their listeners to solve it.

Assume a 20" diameter tank, perhaps 40" long. Let's leave a little gap at the top for fuel expansion and such. Where do you put the mark on a dipstick for a quarter tank, in inches?

I hated math, until I started running into real-world applications like this, and now I wish I'd paid a lot more attention! BTW, my dad is a high school math teacher, and he was stumped too. Thanks! :-)
Jun 23, 2011. 12:54 PMespdp2 says:
I'm trying to solve the "Quarter Tank Problem," where segment area is known, and I need to solve for length, "L", which is where the notch on the dipstick should go.
Jun 20, 2011. 9:37 AMespdp2 says:
Yes, I should have paid more attention indeed. See here:

http://www.mathopenref.com/arcradius.html

I'm trying to find "H" height. I've forgotten my math formula magic. :-/
Jan 30, 2009. 10:31 AMunigamer says:
pi is irrational and is therefore by definition infinite. A clear instructable though.
Jun 20, 2011. 8:56 AMespdp2 says:
Love that quote! Sometimes "good enough" is good enough.
Jan 30, 2009. 7:56 AMuguy says:
Pie are round.
Dec 5, 2009. 11:46 PMPoppa Chubby says:
Cornbread are square.
Mar 17, 2009. 6:48 PMEaglesNestOne says:
EHYOOO 1000th view!!1 and first rating. <3 Verniers
Mar 10, 2009. 7:11 PMFunkNattidelic says:
we did this in school just recently, this instructable would have been helpful about 2 months ago XD but great instructable, i like it !!
Jan 30, 2009. 2:21 AMTransquesta says:
Excellent. I wish I'd had the benefit of such clear explanation in grammar school math classes. . . . . .And in high school. . . . . .And in college. . . :-) Seriously, 'math (or even geometry as the case may be)' evokes that 'special' kind of terror in the hearts of students with which only public speaking can compare! According to most studies I've read, the fear of DEATH pales by comparison.

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Author:KEUrban
I am an administrator at a college, responsible for academic and student affairs. In a previous life, I was a human factors engineer and human performance researcher. I have post-graduate degrees in ...
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