Why and how to work out the volume of a cylinder

July 6, 201246 Comments

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:






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Comments (46)

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  1. 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.

  2. 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

  3. 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?

  4. Theresa Pinder says:

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

  5. Lyndsay Clark says:

    Thank you so much.

  6. 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

  7. Leelaram Khatri says:

    Thanks for your Calculation I was forget about this calculation .

  8. xSoundless Echox says:

    I decided I will take down notes to my copy because these informations are
    really usefull, thank you 😀

  9. 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

  10. 890slay says:

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

  11. RandomStuff Nation says:


  12. Ahmed Alazri says:

    Sir, can you do pythagoras

  13. Ahmed Alazri says:

    Thank you sir !!

  14. 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

  15. Adeyemi Fakoya says:

    Thank you so much, that was a good reminder.

  16. nicole anne polita says:

    where did the 113.112 from ?

  17. Kalyani Choudhury says:

    i hope i do good with my studies with your support

  18. Kalyani Choudhury says:

    thanks simon

  19. Sherryl Busante says:

    ahhhhhh… hello simon i just want to know that how to find the high of a
    cylinder ??? pllzzzz help me ..

  20. 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!

  21. 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!

  22. Susana Marcial says:

    Was so very helpful! Thank you for uploading!!

  23. Antonieta Álvarez says:

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

  24. F Murad Ali says:

    thanq u very much..for shearing knowledge..

  25. 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.

  26. BigBangTheoryBB says:

    Love the drawing. This helped. Thanks so much!

  27. 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.

  28. Ryan Hack says:

    Thank you, helped a lot

  29. 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???????

  30. Mikail Baysan says:

    you ripped of mr collins our colliun who art in hgeaven hallowed be thy
    brackets ! >:(

  31. Andy Baah says:

    Thanks this helped a lot :)

  32. 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

  33. dexmatic says:

    A very good video.

  34. dexmatic says:

    A very good video.

  35. srsly Bailey says:

    Pi is not 3.142 its 3.14

  36. Ismael Djibrilla says:

    Thank you so much :)

  37. Desmone Stevens says:

    This video was very helpful ,

  38. ivan alvarez says:

    thanks helped out big time like all the details and exlpaning

  39. Rasha Becton says:

    Helped my kids alot

  40. Lalay Corea says:

    Youtube is much easier than reading… lol

  41. Jay Driscoll says:

    really helped thanx

  42. matthew bacon says:


  43. Ansa Ahmad says:

    Thank you Sir, This really helped me.

  44. 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

  45. Clara Beavan says:

    How do you work out the volume of a cylinder when it has a thickness for example…..
    Diameter- 6.5
    and an extra added thickness of 0.5??/

  46. Simon Deacon says:

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

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