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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 298

Give examples of geometric solids bounded by one, two ,three , four planes (or parts of planes)

I only need help with the 1 plane one.

I'm not sure of it but the only one I can come with is a sphere. I know that it's surface isn't flat( the question doesn't mention that it needs to be flat) , or I'm not even sure that it's composed of a plane since it can't be decomposed.

SO my real question would be : Can we consider the sphere composed of only 1 plane or not ? Even if we can't decompose it ?

Any suggestions ?

I don't want the answer to the question, just hints-suggestions. Thank you

*Last edited by Al-Allo (2013-08-18 11:33:24)*

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,740

I'm not sure what the question means exactly. What did you get for the others?

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 298

Two: cone

three: Cylinder

Four: Pyramid with triangular base

I thought also for the first one half a sphere, if we only count it's base but not its lateral surface.. (Because im not sure if the lateral face of a sphere is a plane or not...)

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,740

Hi

Thanks for that. I can understand why the triangular based pyramid is four. Each face is a plane.

I don't understand the other two.

Why is a cylinder 3? The ends are planes (that's two ) but the curved surface isn't even flat so it isn't a plane.

Is this because you have used the word 'plane' where you meant 'surface'?

http://www.mathsisfun.com/definitions/plane.html

http://www.mathsisfun.com/definitions/surface.html

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 298

Well yes that's it. If we decompose it, we get 3 surfaces.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,740

I've just edited my post by adding two links.

One of then will give you the hint you require.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 298

ok, so i've got half a cylinder. which is composed of two half a circle and one rectangle.

half a cone which is composed of one triangle and half a circle

and half a sphere with only one circle

is this it ??

*Last edited by Al-Allo (2013-08-19 03:48:51)*

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**bob bundy****Moderator**- Registered: 2010-06-20
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I'm still not sure. What language was the question written in?

Bob

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 298

Well, it's originaly a russian book, but it's in english. (If I understood correctly your question?)

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,740

And the word used is definitely 'plane'?

Bob

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 298

Yes, I copied the question word for word

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**bob bundy****Moderator**- Registered: 2010-06-20
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OK. Then I will assume that the original Russian also meant plane ie. flat surface.

In which case triangular pyramid is good for four planes.

The curves surfaces are not planes so you cannot count them.

But the question does not say that the planes must be the only bounds; only that it must be bounded by a plane or planes.

The hemi-sphere seems a good answer for one plane; the other boundary is not a plane but we are not asked about that.

Cylinder seems good for two planes (the ends; the curved part we ignore as it isn't a plane.)

So we just need a 3 plane example.

Imagine a sphere, centred on the origin. (3D coordinates so x, y and z) Now cut away everything that has a negative coordinate so you are left with one eighth of a sphere bounded by the x-y, x-z and y-z planes. That is the three planes we are seeking.

Below: best image I could find. No idea what it's called.

Hope that helps.

Bob

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 298

But for the semi-cylinder, you didn't count the rectangle ????

*Last edited by Al-Allo (2013-08-19 04:31:22)*

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,740

You're right! I'd forgotten that one. Ok. You have them all.

Bob

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 298

ok Thank you for your help ! It was great !

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