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How to work out the volume of a cone and hemisphere

May 6, 2013 by Simon 24 Comments

– or an ice cream! … which is just the volume of a cone and hemisphere, added together 🙂

How to work out the volume of a cone and hemisphere – or an ice cream!These are really higher level grade 5 – 6 GCSE questions but:

– the formulas are given on the exam paper (although you should learn them :-))

and

– if you work through logically it should be straightforward.

The questions usually involve calculating a volume of a cone, sphere or hemisphere. There might be a couple of ‘curve balls’ such as different units, diameters given etc.

Download the Quick Test here

 

Volume of a cone

Volume of a cone

 

 

 

 

where

r is the radius at the base

h is the height

pi is given in the exam paper (usually 3.142)

 

Volume of a sphere (a ball)

How to calculate the volume of a sphere

 

 

 

 

where r is the radius

pi is given in the exam paper (usually 3.142)

A hemisphere is just half a sphere so you can calculate the total and then divide by two.

 

Putting it all together!

So, how big is an ice cream?

I calculated around 330 cm³ and it was great fun – have you ever tried measuring an ice cream?!

 

Watch the videos on YouTube

How to work out the volume of a cone 

How to work out the volume of a hemisphere

How to calculate the volume of a cone and hemisphere 

Comments

  1. Stella says

    August 19, 2016 at 3:58 pm

    Although this video was very helpful and i understand, I have a My Maths question which has the height of the cone and hemisphere but no measurement for the diameter, how would i find the volume ? I’m am stuck in my tracks lol SOS

    Reply
    • Simon Deacon says

      August 19, 2016 at 8:20 pm

      Hi – thanks for your comment, happy to help but I’d really need to see the question. You would need some way of working out the radius, to be able to calculate the volume …. All best S 🙂

      Reply
  2. Brian Luong says

    July 10, 2015 at 8:57 pm

    That was really helpful! Thanks so much for your help!

    Reply
  3. Toprak Åžen says

    June 23, 2015 at 9:21 pm

    +N7 RiZe Is that Movilla Petru? lol

    Reply
  4. Umar Ejaz says

    June 7, 2015 at 11:39 pm

    What do you do if the height is the length of the cone and hemisphere? How
    do you work the height of the cone itself?

    Reply
  5. lee dickenson says

    June 7, 2015 at 9:27 pm

    Great thank you for the tutorial.

    Reply
  6. Mark Fuzuzu says

    June 3, 2015 at 11:27 pm

    oh my God that jumpscare at 4:14

    Reply
  7. Antonio Akridas says

    May 31, 2015 at 8:41 pm

    This was really helpful, thanks a lot

    Reply
  8. timothy handy says

    May 3, 2015 at 1:55 am

    I got 376.8
    which is 377

    Reply
  9. Brittany Dannhauser says

    January 11, 2015 at 2:05 pm

    Thank you very much Simon! I wish we had more math teachers like you in our
    schools.

    I was wondering if you could post a video on how to find the volume of the
    amount of ‘water’ in a shape. Sometimes theres (im using an example) a
    picture of a triangular shape with a height of 15cm, and a radius of 9cm.
    It has water in it with a height of 8cm. (I hope im not confusing you!) How
    would you work that out?

    Thanks!

    Reply
  10. Brittany Dannhauser says

    January 11, 2015 at 2:04 pm

    Thank you very much Simon! I wish we had more math teachers like you in our
    schools.

    I was wondering if you could post a video on how to find the volume of the
    amount of ‘water’ in a shape. Sometimes theres (im using an example) a
    picture of a triangular shape with a height of 15cm, and a radius of 9cm.
    It has water in it with a height of 8cm. (I hope im not confusing you!) How
    would you work that out?

    Thanks!

    Reply
  11. Prakash sarala says

    December 9, 2014 at 5:50 am

    how is calculate the area for the uneven diagram with out dimensions?
    sir plz tell earliest

    Reply
  12. Prakash sarala says

    December 8, 2014 at 9:39 am

    THIS VIDEO IS VERY USEFUL THANQ

    Reply
  13. Prakash sarala says

    December 8, 2014 at 9:36 am

    HOW IS CALCULATE THE UNEVEN DIAGRAM WITH OUT DIMENSION ?

    Reply
  14. AVeryRandomMegan says

    November 3, 2014 at 4:28 pm

    What if the height given is for the cone and the hemisphere?

    Reply
  15. Rainbow Cummings says

    July 20, 2014 at 12:51 am

    Why cm cubed and not just cm?

    Reply
  16. MrWill1729 says

    February 23, 2014 at 4:53 pm

    i gave you a like because you said football not soccer 🙂

    Reply
  17. joshua ray says

    January 16, 2014 at 4:54 pm

    How about if the measurements were given in terms of r?

    Reply
  18. CL lokesh kumar says

    August 30, 2013 at 9:12 am

    nice

    Reply
  19. Sienna Nealon says

    May 25, 2013 at 3:38 am

    Someone who helps! Thanks!

    Reply
  20. Simon Deacon says

    April 27, 2013 at 11:30 pm

    That’ s great, thanks for letting me know 🙂

    Reply
  21. tim nyams says

    April 27, 2013 at 10:48 pm

    Merci beacoup, this help me a lot, Merci

    Reply
  22. Samer Dib says

    April 12, 2013 at 2:57 am

    thank you

    Reply
  23. Eumesh Weerapura says

    April 9, 2013 at 1:13 am

    Thank you very much Sir.

    Reply

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