Why and how to work out the volume of a cylinder

July 6, 201227 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 (27)

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    1. 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!

    2. 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!

    3. Susana Marcial says:

      Was so very helpful! Thank you for uploading!!

    4. Antonieta Álvarez says:

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

    5. F Murad Ali says:

      thanq u very much..for shearing knowledge..

    6. 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.

    7. BigBangTheoryBB says:

      Love the drawing. This helped. Thanks so much!

    8. 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.

    9. Ryan Hack says:

      Thank you, helped a lot

    10. 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???????

    11. Mikail Baysan says:

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

    12. Andy Baah says:

      Thanks this helped a lot :)

    13. 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

    14. dexmatic says:

      A very good video.

    15. dexmatic says:

      A very good video.

    16. srsly Bailey says:

      Pi is not 3.142 its 3.14

    17. Ismael Djibrilla says:

      Thank you so much :)

    18. Desmone Stevens says:

      This video was very helpful ,

    19. ivan alvarez says:

      thanks helped out big time like all the details and exlpaning

    20. Rasha Becton says:

      Helped my kids alot

    21. Lalay Corea says:

      Youtube is much easier than reading… lol

    22. Jay Driscoll says:

      really helped thanx

    23. matthew bacon says:


    24. Ansa Ahmad says:

      Thank you Sir, This really helped me.

    25. 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

    26. 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??/

    27. Simon Deacon says:

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

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