# Why and how to work out the volume of a cylinder

## How to work out the volume of a cylinder is typically a grade C GCSE question..

GCSE Grade C question to calculate the volume of a cylinder with a radius of 3cm and a height of 4cm.

How to work out the volume of a can of coke. Just a quick video to calculate if 330ml is accurate. It is… but my estimation shows 380ml ! I’ve not allowed for the coke can design and not measured too accurately. Although I hope it helps to get an idea of working out the volume of a ‘real’ cylinder.

##### Try the Quick Test circles and cylinders

A cylinder can be any size but it must have a circular top and base.

They are used in many different ways from cake boxes to transporting fuel.

Examples of cylinders are oxygen, gas, flask, pipe, bin, vase, engine, cup, torch, computer hard drive, shock absorber, can of baked beans, packet of biscuits, lamp post and candle. Contact us with any more suggestions!

It could be very important to find out a volume -

- to avoid overfilling
- using too much material
- working out the cost
- calculating the flow, pressure, density, mass
- and so on…

The two measurements you will need to find are:

**Height** – usually given in the question – and **area. **

Make sure that the units are the same i.e. centimetres or metres.

##### Calculate the area of the circle first …. by using the formula

- this is pronounced as ‘pi r squared’
- pi is usually 3.142
- r is the radius of the circle

Note that ‘r squared’ means ‘**radius x radius’** (NOT 2 x the radius!).

##### ….. and then multiply by the height.

So, for a radius of 5cm and a height of 10 cm:

Area of circle is ‘pi r squared’

so pi x 5 x 5

which = 3.142 x 5 x 5

###### Therefore, area of end circle = 78.55 cm squared

Then multiply the area of the circle by the height of the cylinder -

= 78.55 x 10

##### Therefore, total volume of cylinder = 785.5 cm cubed

Watch the videos on YouTube:

https://www.youtube.com/watch?v=ENnFJXk67xk

https://www.youtube.com/watch?v=yeeWRYMxp_0

https://www.youtube.com/watch?v=r-6m6GLqK7E

https://www.youtube.com/watch?v=WddhEd9bk0o

Visit other related posts:

Filed in: Higher • Maths Videos

Thank you so much, I have the CAHSEE in 2 days and I needed to study and I

forgot about how to calculate volume of a cylinder!

Hi Simon,

I actually just completed a lab very similar to this. Your approximation of

the soda can volume, (380 mL), is actually pretty close. There is a small

pocket of air within the can, which allows for a certain degree of error

during the filling process. This also makes unopened cans “almost”

positively buoyant. Thanks!

Was so very helpful! Thank you for uploading!!

OMG seriusly u are the best teacher ever I need u in my lessons of maths

thanq u very much..for shearing knowledge..

Hello Simon that was really a great help. Can you please do a tutorial for

finding volume of a metal hollow cylinder.

Love the drawing. This helped. Thanks so much!

Simon Deacon can you do a tutorial for some hard percentages like 23่

percent or something like that plz.i am having a hard time learning about

them thx.

Thank you, helped a lot

cylindrical area formula two types available one is 3.14 X r X r .another

one formula also (3.14 x D x D) / 4 are u know???????

you ripped of mr collins our colliun who art in hgeaven hallowed be thy

brackets ! >:(

Thanks this helped a lot

Thanks u r my maths hero never knew how to do until you did the questions

so I can understand thanks alot

A very good video.

A very good video.

Pi is not 3.142 its 3.14

Thank you so much

This video was very helpful ,

thanks helped out big time like all the details and exlpaning

Helped my kids alot

Youtube is much easier than reading… lol

really helped thanx

thx

Thank you Sir, This really helped me.

Hi Clara – thanks for the question. Probably the easiest is to calculate two cones, one with the thickness added, the other as the smaller cone. Then subtract one from the other. There’s a similar question (?) on How to calculate the volume of a hemisphere video. Is that OK? If not, please email through mathswrap and I’ll try to help. All best S

How do you work out the volume of a cylinder when it has a thickness for example…..

height-21cm

Diameter- 6.5

and an extra added thickness of 0.5??/

Hi – I manage 3 First Class Learning tutoring centres in North Leeds.