## How to work out the volume of a cylinder is typically a grade 4 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

andrew moon says

Hi simon you are a great teacher but the flickering of light and the

constant focusing of your camera makes it difficult for me to concentrate

on your video’s.

Chandraprakash G says

Volume (3d) = Base Area (2d) * Height (golden word i was searching for !!)

Thanks Prof +Simon Deacon !!

One suggestion is, please tell them cm3 = milliliter (i.e) 1000 cm3 = 1

Liter, would be easy to understand the unit better that way.

Example: 113 cm3 = 113 ml

Scot Inman says

Why is it when you use different calculators (TI-30XS) when you use the Pi

button to set u the problem you get a different answer?

Theresa Pinder says

Thank you for helping me to understand how to fine the volume of a

cylinder.

Lyndsay Clark says

Thank you so much.

mr serious topics 131 helping the people says

you my friend are a maths prodigy thanks so much for all your help my exam

is next week Thursday i just want to say if i get a C grade its because of

your help so thank so much because i was always working at grade D and you

have help a lot lets hope i get the grade C in the exam

Leelaram Khatri says

Thanks for your Calculation I was forget about this calculation .

xSoundless Echox says

I decided I will take down notes to my copy because these informations are

really usefull, thank you 😀

Benjiiay B says

you forgot to times the top circle by 2 as theirs also the one on the

bottom meaning the answer is wrong

890slay says

Simple and to the point. You, sir, know your stuff.

RandomStuff Nation says

:]

Ahmed Alazri says

Sir, can you do pythagoras

Ahmed Alazri says

Thank you sir !!

Zubee Okafor says

Thats pretty cool. I am working on assignment to measure about 50 cans. I

have to agree that his have definitely made things much easier. Thanks

heaps!!!

Adeyemi Fakoya says

Thank you so much, that was a good reminder.

nicole anne polita says

where did the 113.112 from ?

Kalyani Choudhury says

thanks

i hope i do good with my studies with your support

Kalyani Choudhury says

thanks simon

Sherryl Busante says

ahhhhhh… hello simon i just want to know that how to find the high of a

cylinder ??? pllzzzz help me ..

UberPootis says

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!

Gregory Burrill says

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!

Susana Marcial says

Was so very helpful! Thank you for uploading!!

Antonieta Álvarez says

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

F Murad Ali says

thanq u very much..for shearing knowledge..

Anwesha Bhattacharya says

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

finding volume of a metal hollow cylinder.

BigBangTheoryBB says

Love the drawing. This helped. Thanks so much!

Nerf Leader says

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.

Ryan Hack says

Thank you, helped a lot

Prakash sarala says

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???????

Mikail Baysan says

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

brackets ! >:(

Andy Baah says

Thanks this helped a lot 🙂

Sandith Elegoda says

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

so I can understand thanks alot

dexmatic says

A very good video.

dexmatic says

A very good video.

srsly Bailey says

Pi is not 3.142 its 3.14

Ismael Djibrilla says

Thank you so much 🙂

Desmone Stevens says

This video was very helpful ,

ivan alvarez says

thanks helped out big time like all the details and exlpaning

Rasha Becton says

Helped my kids alot

Lalay Corea says

Youtube is much easier than reading… lol

Jay Driscoll says

really helped thanx

matthew bacon says

thx

Ansa Ahmad says

Thank you Sir, This really helped me.

Simon Deacon says

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

Clara Beavan says

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??/

Simon Deacon says

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