Why and how to work out the volume of a cylinder

July 6, 201217 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

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

 

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  • Why and how to work out volume of a prism
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    Comments (17)

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    1. Mikail Baysan says:

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

    2. Andy Baah says:

      Thanks this helped a lot :)

    3. 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

    4. dexmatic says:

      A very good video.

    5. dexmatic says:

      A very good video.

    6. srsly Bailey says:

      Pi is not 3.142 its 3.14

    7. Ismael Djibrilla says:

      Thank you so much :)

    8. Desmone Stevens says:

      This video was very helpful ,

    9. ivan alvarez says:

      thanks helped out big time like all the details and exlpaning

    10. Rasha Becton says:

      Helped my kids alot

    11. Lalay Corea says:

      Youtube is much easier than reading… lol

    12. Jay Driscoll says:

      really helped thanx

    13. matthew bacon says:

      thx

    14. Ansa Ahmad says:

      Thank you Sir, This really helped me.

    15. 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

    16. 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??/

    17. Simon Deacon says:

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

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