The Cone and Cylinder Debate!

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Written by Holly (Teach Starter)

Who would have thought that the properties of the cone and cylinder would cause such a stir in the Teach Starter office? But, they certainly did some time ago! As teachers, a lot of us taught our young students that cones and cylinders have edges and faces. Anyone else?

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However, this is no longer the case and there is a mathematical reason behind this change!

Male mathematics teacher


Why Do Cylinders and Cones Not Have Edges or Faces?

As teachers, we thought the best place to look to clear up the debate would be the Australian curriculum. However, like a lot of sites, it wasn’t very clear why cones and cylinders do not have edges or faces.

We found the NSW syllabus outlines the language that should be used the classroom around this topic to be very clear, Hence, we are using this as our source of information:

  • In geometry, the term ‘face’ refers to a flat surface with only straight edges, as in prisms and pyramids, eg. a cube has six faces.
  • Curved surfaces, such as those found in cylinders, cones, and spheres, are not classified as ‘faces’.
  • Similarly, flat surfaces with curved boundaries, such as the circular surfaces of cylinders and cones, are not ‘faces’.
  • In geometry, the term ‘edge’ refers to the interval (straight line) formed where two faces of a three-dimensional object meet.
  • The NSW Syllabus describes a cylinder as a 3D object that has two flat surfaces, one curved surface, no faces, no edges and no vertices.

It’s really important that children grasp the difference between prisms, pyramids, cubes and cones, cylinders and spheres. By understanding the mathematical definitions of the language used to describe the properties of 3D objects, your students are being set up for success.

Resources to get you started:

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Comments & feedback

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Hello, So if cylinders and cones do not have an edge what do you call that part where the two sides meet?? It exists therefore needs a name. And what do you call the circular face if only a face has straight sides?
Thanks Raylene

Raylene Bowtell · Jul 17th, 2020

Hi Raylene,

A ‘circular face’ is referred to as a flat surface in the NSW syllabus. As for the ‘edges’ of cones and cylinders, the NSW syllabus doesn’t explicitly state what they are called. It refers to the objects’ circular faces as having curved boundaries, but does give a name to their ‘curved edges’.
Naming this type of feature could be a fun activity for your students! Have them come up with a cool new name and pitch it to the class.

Tom (Teach Starter) · Jul 17th, 2020

What does the Australian curriculum say about this? I tried to find it on their website but with no luck.

Kathymc1 · May 7th, 2020

Hi Kathy,

The Australian Curriculum does’t really give us much clarification on this topic. The blog outlines the NSW terminology, but the Australian Curriculum only mentions faces, corners and edges.
So it seems like the debate rages on!
If we can assist you with anything else, please don’t hesitate to get in touch!

Tom (Teach Starter) · May 8th, 2020

Hi Jeremy, this was written some time ago however the information is still exactly the same. We found this information – https://education.nsw.gov.au/teaching-and-learning/curriculum/key-learning-areas/mathematics/Early-Stage-1-to-Stage-3/resources/diagnostic-tasks/3d-shape–sort-and-classify. I hope that is helpful. Thanks for your message.

Holly (Teach Starter) · May 5th, 2020

So is the point of the cone a vertex or apex? Cheers

Alba Aparicio · Sep 7th, 2018

Hi Alba, I believe it’s an apex.

Holly (Teach Starter) · Sep 14th, 2018

I am wondering the same thing. I thought Apec and vertex were the same thing, but does the cone have one if it does not have edges? I think the answer is “no”.

Tracey Keynes · May 6th, 2019

When I did my teaching, I found also confusing with cone and cylinder. No edges and vertices ? and only faces?

Marcelino Simamora · Jul 31st, 2018

Hi Marcelino,
I am glad this blog could help you with defining the properties of these two objects.
If there is anything else we can assist you with, please don’t hesitate to contact me.

Kristian · Aug 10th, 2018

The posters in your shape set still have a sphere as having one face… given what you have decided above does this need to be updated?

Polly Alexander · Feb 28th, 2018

Hi Polly,
Thanks so much for notifying us of this. We have now updated that resource to reflect the information in this blog. Have a lovely day!

Holly (Teach Starter) · Feb 28th, 2018

Thanks for the correct terminology ! its great to have resources that reflect the current information.

Sharon Hayman · Mar 31st, 2017

Thanks for your comment Sharon 🙂

Holly (Teach Starter) · May 20th, 2017

So pleased the labeling of these 3D objects has been brought to everyone’s attention. Many available resources don’t apply the correct terms.

Elisabet Kovacevic · Mar 30th, 2017

Thanks for your comment Elizabet!
Kind regards,
Holly

Holly (Teach Starter) · Mar 30th, 2017

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