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Why and how to work out the volume of a cylinder

July 6, 2012 by Simon 46 Comments

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

pirsquared

  • 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

 

 

Comments

  1. andrew moon says

    August 5, 2015 at 4:01 am

    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.

    Reply
  2. Chandraprakash G says

    July 25, 2015 at 6:56 pm

    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

    Reply
  3. Scot Inman says

    July 7, 2015 at 8:38 pm

    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?

    Reply
  4. Theresa Pinder says

    June 17, 2015 at 1:17 am

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

    Reply
  5. Lyndsay Clark says

    June 2, 2015 at 9:47 pm

    Thank you so much.

    Reply
  6. mr serious topics 131 helping the people says

    May 30, 2015 at 2:59 pm

    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

    Reply
  7. Leelaram Khatri says

    May 28, 2015 at 12:37 pm

    Thanks for your Calculation I was forget about this calculation .

    Reply
  8. xSoundless Echox says

    May 19, 2015 at 9:23 pm

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

    Reply
  9. Benjiiay B says

    April 19, 2015 at 9:37 pm

    you forgot to times the top circle by 2 as theirs also the one on the
    bottom meaning the answer is wrong

    Reply
  10. 890slay says

    April 11, 2015 at 7:29 pm

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

    Reply
  11. RandomStuff Nation says

    April 7, 2015 at 5:48 pm

    :]

    Reply
  12. Ahmed Alazri says

    March 22, 2015 at 10:38 pm

    Sir, can you do pythagoras

    Reply
  13. Ahmed Alazri says

    March 22, 2015 at 10:37 pm

    Thank you sir !!

    Reply
  14. Zubee Okafor says

    March 21, 2015 at 3:20 am

    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!!!

    Reply
  15. Adeyemi Fakoya says

    March 19, 2015 at 8:56 am

    Thank you so much, that was a good reminder.

    Reply
  16. nicole anne polita says

    February 22, 2015 at 11:16 am

    where did the 113.112 from ?

    Reply
  17. Kalyani Choudhury says

    February 8, 2015 at 8:18 pm

    thanks
    i hope i do good with my studies with your support

    Reply
  18. Kalyani Choudhury says

    February 8, 2015 at 8:07 pm

    thanks simon

    Reply
  19. Sherryl Busante says

    February 6, 2015 at 1:41 am

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

    Reply
  20. UberPootis says

    February 1, 2015 at 3:43 pm

    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!

    Reply
  21. Gregory Burrill says

    January 25, 2015 at 11:10 pm

    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!

    Reply
  22. Susana Marcial says

    January 22, 2015 at 7:41 pm

    Was so very helpful! Thank you for uploading!!

    Reply
  23. Antonieta Álvarez says

    December 27, 2014 at 2:35 pm

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

    Reply
  24. F Murad Ali says

    December 7, 2014 at 7:15 am

    thanq u very much..for shearing knowledge..

    Reply
  25. Anwesha Bhattacharya says

    November 23, 2014 at 3:26 pm

    Hello Simon that was really a great help. Can you please do a tutorial for
    finding volume of a metal hollow cylinder.

    Reply
  26. BigBangTheoryBB says

    November 5, 2014 at 12:30 am

    Love the drawing. This helped. Thanks so much!

    Reply
  27. Nerf Leader says

    October 15, 2014 at 1:46 pm

    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.

    Reply
  28. Ryan Hack says

    September 28, 2014 at 1:26 pm

    Thank you, helped a lot

    Reply
  29. Prakash sarala says

    September 24, 2014 at 2:47 pm

    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???????

    Reply
  30. Mikail Baysan says

    August 7, 2014 at 11:48 am

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

    Reply
  31. Andy Baah says

    June 5, 2014 at 8:05 pm

    Thanks this helped a lot 🙂

    Reply
  32. Sandith Elegoda says

    May 27, 2014 at 3:48 pm

    Thanks u r my maths hero never knew how to do until you did the questions
    so I can understand thanks alot

    Reply
  33. dexmatic says

    May 12, 2014 at 12:07 am

    A very good video.

    Reply
  34. dexmatic says

    May 12, 2014 at 12:07 am

    A very good video.

    Reply
  35. srsly Bailey says

    May 7, 2014 at 10:28 pm

    Pi is not 3.142 its 3.14

    Reply
  36. Ismael Djibrilla says

    March 31, 2014 at 3:28 am

    Thank you so much 🙂

    Reply
  37. Desmone Stevens says

    March 26, 2014 at 12:43 pm

    This video was very helpful ,

    Reply
  38. ivan alvarez says

    March 19, 2014 at 7:37 pm

    thanks helped out big time like all the details and exlpaning

    Reply
  39. Rasha Becton says

    March 11, 2014 at 12:33 am

    Helped my kids alot

    Reply
  40. Lalay Corea says

    February 19, 2014 at 4:04 pm

    Youtube is much easier than reading… lol

    Reply
  41. Jay Driscoll says

    February 18, 2014 at 7:49 am

    really helped thanx

    Reply
  42. matthew bacon says

    January 12, 2014 at 9:57 pm

    thx

    Reply
  43. Ansa Ahmad says

    November 10, 2013 at 2:52 pm

    Thank you Sir, This really helped me.

    Reply
  44. Simon Deacon says

    May 13, 2013 at 10:19 pm

    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

    Reply
  45. Clara Beavan says

    May 13, 2013 at 9:40 pm

    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??/

    Reply
  46. Simon Deacon says

    March 19, 2013 at 12:37 pm

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

    Reply

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