# Volume of a Cylinder

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## Introduction: Volume of a Cylinder

There is more than one way to calculate volume. This Instructable will show you how to calculate volume using water.

I selected this empty can because I wanted to know its internal volume.

First, I dried the can out with a towel and made sure that it was clean.

## Step 1: Place Empty Can on Scale.

Next , I placed the can on a scale and changed the units to grams.

This can happens to have a mass of 48 grams.

## Step 2: Tare Out the Empty Can.

My scale has a nifty feature that lets you tare out the mass of the scale.

I pressed the tare button and the scale resets back to zero with the can still resting on the scale.

## Step 3: Fill With Water.

Now, I filled the can with water up to the brim. I made sure that I did not spill any.

The mass of the water in the can is 454 grams. This is the true mass of the water because the mass of the can was already accounted for.

Ok, here is how I can figure out the volume of the can. The density of water is 0.9982 g/cc at 68 degrees Fahrenheit.

If we take the weight of the water, 454 grams and divide this by the density of the water at 68F we will be left with the volume of the water.

454 grams / 0.9982 g/cc = 454.8 cubic centimeters of water.

This turns out to be 15.38 ounces of volume for this particular can.

Using this same technique the volume of a sphere or any enclosed object can be calculated.

That is how you can find the volume of a cylinder using water. I hope you enjoyed this Instructable.

While your at it check out my other Instructables:

https://www.instructables.com/id/Digital-Measurment-Estimator/
https://www.instructables.com/id/Hanging-around/
https://www.instructables.com/id/476_better_than_a_Bank/

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## Questions

You should also realise that since your scales only read to the nearest gram, the volume you calculated is only accurate to 3 significant figures at best ( ie, 15.4 fl.oz., not 15.38). I note your comments that you were not looking to achieve high precision, but in that case you should report your results only to the degree of accuracy that your method allows. Likewise using density values for water of 5 significant figures is unnecessary when your scales are two orders of magnitude less accurate. Just something to be aware of when taking scientific measurements.

If you know the radius or the circumfrence and the hieght of the can you can calculate the volume by the formula- pi * r(radius)^2 * h
for eg if the height is 7m and radius is 2m then it goes like this
22/7 * 2 * 2 *7=88 Meter cube

Good stuff. The only issue is you measured the capacity volume of the can, not the can. The can's volume found using water is by using a graduated container larger than the can, filled with water. Set the water at a desired height and then submerse the can. The difference in volume is the volume of the can. Sorry. Just being nitpicky. By the way. 68 F is 20 C

Yes you are correct, I did not specify that I am measure the internal volume of the can. Thanks

68oF is about 25oC - was this the temperature you weighed the can at? (it's a bit warm for where I live)

Also, "ounces" are units of weight unless you mean fluid ounces.

L

(interesting user name)

2 replies

Thanks for looking at my Instructable. I appreciate your comments and I would like to respond to your concerns.

I made a couple of assumptions that maybe I shouldn't have. I thought since the subject was volume it was naturally assumed units of measure to be fluid ounces rather than ounces in weight.

My second assumption was regarding the temperature. The temperature was not recorded at the time of measure. I did test inside with the air temperature of about 72 degrees, however the water was straight out of the tap and was probably about 55 degrees or so.

If you are interested, below is a link showing some the density of water at various temperatures.
I used the temperature that best matched my ambient air/water temperature.

As you can see the density of water at 100c is 0.95836 g/cc as compared to 0c of 0.99984 g/cc Water is 4.14% less dense at boiling than at freezing. So yes there would be some error due to effects of temperature.

Another error that I failed to account for is the use of a kitchen scale. This is hardly what I would consider to be accurate. Since there would be error associated with this device as well the total volume of water in the can is approximately close to what the true volume of the can.

I suspect that because the temperature of the water was at approximately 55 degrees F and making the assumption that the scale is accurate the actual volume of the can would be slightly larger than what I calculated above.

The intended purpose of this Instructable was demonstrate the concept. I really was not trying to achieve a fine degree of accuracy including values of uncertainty.

Thanks, I hope this helps,

I read my thermometer wrong last night, 68oF is more like 20oC - I read across from 78 (the 70 isn't printed), so sorry about that.

The level of accuracy is not that important, as long as you know how accurate your method is: it still gives you a volume.
The kitchen scale may or may not be accurate, but it's important to recognise that the precision of the scale is a different thing. And for this volume +/- 1g is less than 0.5%

L