# Is a cylinder a prism?

Discussion in 'Mathematics' started by Fruit Cake, Jan 26, 2008.

1. ### Fruit Cake

Hi, I'm supposed to be teaching prisms in my maths class but I'm slightly confused to whether or not a cylinder is a prism?

2. ### Fruit Cake

Hi, I'm supposed to be teaching prisms in my maths class but I'm slightly confused to whether or not a cylinder is a prism?

3. ### zippy05

a prism is a 3d shape that when bisected creates the same shape....so as long as the result is still a cylinder, or 2 cylinders then its a prism.....that doesn't really make sense does it...hold on.....

"polyhedron with two polygonal faces lying in
parallel planes and with the other faces parallelograms"

not sure that helps much either....but simple answer....yes a cylinder is a prism

5. ### coyoteNew commenter

(I might not be able to remember what day it is, or to set homework, or even to plan lessons, but I can remember contributing to the above thread more than two years ago!)

6. ### Maths_MikeNew commenter

no it is not.

It is not even a polyhedron as a circle is not a polygon.

It does however behave in a similar fashion to a prism - certainly with regard to calculating volume - and may be thought to be "prism-like" even though technically it is not one!

We have had this debate many times before - do a search on this forum

7. ### maths126New commenter

Hmm - technically it is not a prism. It seems I have been teaching it incorrectly for the almost 20 years, but I haven't been sued yet!

The simple school school-level definition of prism with "constant cross section" is certainly adequate for all school-level examinations.

1) The Exam boards themselves use the simple version of "prism" in all their papers. Indeed, the cheesy little illustration on the formula sheet is not even a true prism itself! As far as they are concerned, though, a cylinder would be given a tick if there were a question which said "Tick which of these solids is a prism"

2) The formula for cylinder volume (indeed for a "prism" of any curved boundary cross-section) is identical to that when used for the CSA x Width formula for a True Prism. Finding the volume of such solids by integration gives the same result too.

Nevertheless, I am going to keep telling children that a cylinder is a prism, just as I continue to tell children that you can't find the square root of a negative number. Surely our job is to clarify and simplify their world so that they can build up their understanding as they become more sophisticated. We are always refining the way we look at the world, even as adults. The model we keep in our heads is just being continually modified.

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8. ### Polecat

If the majority of mathematicians and teachers of mathematics regard a cylinder as a prism, then a cylinder is a prism. The usage of words is not fixed. Eventually Chambers, OED and even writers of maths textbooks will have to define the word 'prism' in line with the times.

9. ### emilyisobel

I think that it depends on what point you are trying to achieve.
What are the characteristics of a prism?
What are the characteristics of a cylinder?
Are we trying to make links or distinctions?
If we are trying to make links and thus develop an understanding with regards to volume, then it is somewhat disingenuous to make differences between a cylinder and a prism.
Pendanticism should not get in the way of developing understanding.

Yes, it is.

Yes, it is.

Yes, it is.

Yes, it is.

12. ### frustumEstablished commenter

There's a language issue too: I understand that in some languages, the definition of prism makes no reference to polyhedra, at which point there's no problem with including a cylinder.
I agree that whatever the definition, it's important to link cylinders with prisms, particularly with regard to the volume formula.

13. ### afterdark

Basically a rehash of the is a circle a polygon problem.
Technically a cylinder is not a prism.
Working from the simplistic definition of shapes with uniform cross-section then it would be included.
The volume is still the product of the cross-sectional area and the length.
In this 'sense' it is prism-like.
Given the abstract nature of euclidean geometry I would say you could accept it as a prism, the non polygonal nature of the cross-section aside.
In fact Cambridge university say <u>it is a prism</u> in their IGCSE.
http://www.cie.org.uk/docs/qualifications/new_qualifications/int_maths/Cambridge%20IGCSE%20International%20Maths%202012%20Syllabus.pdf
Quote
"Surface area and volume of prism and pyramid
(in particular, cuboid, cylinder and cone)"
Not only are they including cylinders with prisms they are including cone with pyramids!
Jackpot!
Please redirect all pissy comments to the University of Cambridge.
For anyone teaching IGCSE, like me, sorry it is wrong to say that a cylinder is not a prism.
I wouldn't really mind if the interest in this question was genuine. However I do get a feel that sometimes people post on here with beartrap questions trying to be clever.

14. ### onethingidoNew commenter

But then, it is quite annoying not to be sure what to teach! Especially when the national curriculum contradicts itself:

"Pupils should be taught to:

• derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)"
(implying that cylinders are prisms) and just a bit further on

• "use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D"
(suggesting that they are not).

( https://www.gov.uk/government/publi...d-mathematics-programmes-of-study#key-stage-3 )

It might seem pedantic, but when the topic comes up in the scheme of work, conscientious mathematicians are inclined to try to teach the correct definitions, pedagogical or not.
Is it really necessary to teach children that faces are the flat surfaces of a 3D shape, and then in the same breath say that spheres have 1 face, as BBC Bitesize does?

http://www.bbc.co.uk/education/guides/z83487h/revision

15. ### jonathan_whiteNew commenter

This is how we define a prism in my country:

"Let P be a convex polygon in a plane π and let AB be a line segment not belonging to this plane. The part of space formed by all line segments CD (parallel and congruent to AB) where C is a point belonging to P is called a prism."

This definition is taught to Year 10 students.

16. ### mature_maths_traineeNew commenter

Exactly.
You might want to give the precisely-accurate definition to a few highly-gifted students, but for whole class teaching the above approach is surely, overwhelmingly, best.

MMT

17. ### gnulinuxOccasional commenter

A cylinder is not a prism because some of its 'faces' are not flat! QED.
A cylinder can be thought of as the limit of a suitable sequence of prisms - but it is not itself a prism!
Similarly, a point can be regarded as the limit of a sequence of suitable line segments of reducing length, but a point is not a line segment.

18. ### Maths_ShedOccasional commenter

As has been stated a number of times above, as far as the pupils are concerned of course it is a prism.

19. ### gnulinuxOccasional commenter

Would that be the same pupils that regularly refer to a rhombus a 'dimond'(sic)???

20. ### NewToTeachingOldToMathsLead commenter

It is a circular quasi-prism.

There are occasions when you need to distinguish and say that technically it is not prism, and there are occasions when the distinction is immaterial.

A multi-faceted prism will begin to look and behave like a cylinder long before it actually IS a cylinder (e.g. a 1-millionagonal prism - yes, I did just invent that word, and yes, you all know what I mean - needs to be VERY large indeed before you can discern its edges and facets: at any normal size it will look and behave like a cylinder, even though we all know it's actually a prism), just as a hyper polygon looks and to all practical intents and purposes behaves like a circle.

It's just another of those "approaching infinity" phenomena.

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