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!

Step 1: 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)

Comments

[Amnesia Wes]

(removed by author or community request)

[Amnesia Wes]

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.

[Cooldeal]

What about the thickness of the walls of the cylinder? What if the walls were only thick on some of the sides?

[KEUrban]

This instructable assumes that the walls are infinitely thin, but to answer your question, just measure the inside diameter of the cylinder and then the wall thickness is immaterial.

However, if you measure the outside diameter of a cylinder and calculate the volume, then measure the inside diameter and calculate THAT volume and finally subtract the smaller of the two volumes from the larger you'll be left with the volume of the materials in the walls of the cylinder.

Make sense?

[Cooldeal]

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.

[ariberman]

Good overview. Now, can you show me how to do partial volume calculations in a horizontal cylinder? This seems a lot more tricky.

[KEUrban]

It is a lot more tricky. What you're asking is how to calculate the area of a "circular segment." If you lay a cylinder on its side and fill it partially, the flat surface created by the material in the cylinder describes what's called a chord. The typical way to calculate the area of a circular segment requires that you know the angle between the two lines of radius where the chord intersects the perimeter of the cylinder. See this web site for a computation: http://mathworld.wolfram.com/CircularSegment.html

I am working on an Instructable that approximates the area from the depth of the substance filling the cylinder.

In any case, once you know the area of the filled portion of the cylinder, the volume is found simply by multiplying the area by the length of the cylinder, like I describe in step 4 of this instructable.

[espdp2]

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! :-)

[KEUrban]

I still have the 'ible in progress to approximate the value, but I'm just too busy to pull it together.

Search for something called "Gordon's Approximation" to estimate the area of a circular segment, which you would then multiply by the length to generate volume.

Thanks for your comment.

[espdp2]

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.

[espdp2]

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. :-/

[unigamer]

pi is irrational and is therefore by definition infinite. A clear instructable though.

[KEUrban]

Thanks for the comment! Of course you're absolutely correct. I didn't think adding in another mathematical construct like irrational numbers added anything from an instructional standpoint. My philosophy can be summed up by something I read once: "Why measure with a micrometer when you're going to mark it with chalk and cut it with an axe?"

[espdp2]

Love that quote! Sometimes "good enough" is good enough.

[uguy]

Pie are round.

[Poppa Chubby]

Cornbread are square.

[EaglesNestOne]

EHYOOO 1000th view!!1 and first rating. <3 Verniers

[FunkNattidelic]

we did this in school just recently, this instructable would have been helpful about 2 months ago XD but great instructable, i like it !!

[KEUrban]

Thanks for the comment. I am working on a related Instructable that will be up soon!

[Transquesta]

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.

[KEUrban]

Thanks for the kind words. Glad I could help :-)