## How to work out the volume of a cone and hemisphere – or an ice cream!

These are really higher level grade A / B 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

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)

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

Stella says

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

Simon Deacon says

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 🙂

Brian Luong says

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

Toprak Şen says

+N7 RiZe Is that Movilla Petru? lol

Umar Ejaz says

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?

lee dickenson says

Great thank you for the tutorial.

Mark Fuzuzu says

oh my God that jumpscare at 4:14

Antonio Akridas says

This was really helpful, thanks a lot

timothy handy says

I got 376.8

which is 377

Brittany Dannhauser says

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!

Brittany Dannhauser says

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!

Prakash sarala says

how is calculate the area for the uneven diagram with out dimensions?

sir plz tell earliest

Prakash sarala says

THIS VIDEO IS VERY USEFUL THANQ

Prakash sarala says

HOW IS CALCULATE THE UNEVEN DIAGRAM WITH OUT DIMENSION ?

AVeryRandomMegan says

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

Rainbow Cummings says

Why cm cubed and not just cm?

MrWill1729 says

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

joshua ray says

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

CL lokesh kumar says

nice

Sienna Nealon says

Someone who helps! Thanks!

Simon Deacon says

That’ s great, thanks for letting me know 🙂

tim nyams says

Merci beacoup, this help me a lot, Merci

Samer Dib says

thank you

Eumesh Weerapura says

Thank you very much Sir.