Math Is Fun Forum

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,974

Website

Cutting a cone with a plane

A right cone is cut by a plane parallel to its base into two parts which are equal in volume. In what ratio does the plane divide the axis of the cone?

I did this problem with a CAS but I am not feeling brave enough to do it by hand.

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Cutting a cone with a plane

setup the 2x thing, the whole cone is twice the top part or bottom part, where 0<k<1:

So I guess you go 79.37005% down from top and cut there for half volume.

The ratio of the top axis length to the bottom axis length seems to be about this, can't prove it:

Last edited by John E. Franklin (2014-02-27 04:22:17)

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igloo myrtilles fourmis

Bob

Administrator

Registered: 2010-06-20

Posts: 10,136

Re: Cutting a cone with a plane

Little top cone to whole cone = 1:2  by volume

So by length = 1:cuberoot 2

John:  ??? Axis length.  What do you mean?  Are we still talking about cones?

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Cutting a cone with a plane

erased my dumb rambling.

Last edited by John E. Franklin (2014-02-28 06:09:13)

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igloo myrtilles fourmis

Bob

Administrator

Registered: 2010-06-20

Posts: 10,136

Re: Cutting a cone with a plane

hi John,

Still puzzled.

You got

and so did I, although I've expressed it differently.  Where did  3.84732 come from?

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Cutting a cone with a plane

I'm doing the ratio of top to bottom.
You're doing the ratio of top to the whole thing.

Last edited by John E. Franklin (2014-02-28 06:07:56)

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igloo myrtilles fourmis

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Cutting a cone with a plane

So to get the ratio of top to bottom parts vertically,
I did 1 - (cube root of 2 reciprocalled) and put that in the
#:# where 79.3% : 20.6% and then I hit a few
buttons on my calculator and found the special 48003 eighth root thing
by hitting square 3 times.

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igloo myrtilles fourmis

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Cutting a cone with a plane

Oh, I finally see where your 1:1.2599 thing is!!  Its the top vertical to the whole vertical!!

I was doing a ratio of the top vertical to the bottom vertical.

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igloo myrtilles fourmis

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Cutting a cone with a plane

Hi Agnishom;

Here is the algebra.

Let R be the radius of the cone

c is where the cut should be from the top.

h is the height of the cone.

Times both sides by 3 and clean up a bit.

Times both sides by h^2.

Divide by R^2.

Divide by π.

Add c^3 to both sides

Divide both sides by 2.

Take the cube root.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,974

Website

Re: Cutting a cone with a plane

Thanks JEF, bob bundy and bobbym. I finally did it myself

---

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Cutting a cone with a plane

Hi,

I wanted to post a new topic, but I get an error (clicked preview):

Forbidden

You don't have permission to access /post.php on this server.

Additionally, a 404 Not Found error was encountered while trying to use an ErrorDocument to handle the request.

Any workaround?

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"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,974

Website

Re: Cutting a cone with a plane

It  happens when you want to post something but that hits a particular regex which the server thinks is malicious.

In this case, I would post the content on pastebin and post the link here.

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Cutting a cone with a plane

Hi gAr;

Do not continue to post in that thread. The server is getting ready to bar you.
Log off and reboot. Sometimes that helps.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,974

Website

Re: Cutting a cone with a plane

It doesn't. It will stop you again when you try to post the same thing. I explained you my theory before

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Cutting a cone with a plane

Yes, I think you are right but the above sometimes works for me. Also, in the meantime I can post in the thread.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Cutting a cone with a plane

Hmm, it had some links and some commands, maybe it mistakes it to be SQLi. That error response was more human like, it would be better if a corrective action was prescribed! That IP address is banned for now, I could login only after rebooting the router.

I'll try again with some modifications.

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"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Cutting a cone with a plane

You were probably given a new IP. That is what allowed you to log in. This has nothing to do with MIF. It is a problem with the server that we run on. I have been barred at least 3 times and so have 3 others.

Can you give me the barred IP, I will have MIF remove it from the server.

From now on, if you receive that message once, do not keep trying. After 3 or 4 times the server will identify you as a malicious threat.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Cutting a cone with a plane

Oh, okay, I thought it was under MIF's control!

I did not note my old IP addresses, one was barred yesterday also. After removing the url tags and one tilde, I could post it.

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"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Cutting a cone with a plane

Please post it for me if you can.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Cutting a cone with a plane

I have posted it.

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"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Cutting a cone with a plane

Sorry, I meant the IP address. In the future write it down and I will PM MIF. He can access the server, I can not.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Cutting a cone with a plane

I think it's not possible for me since the router doesn't save the history on reboot. I get only a local IP addr, so my machine's history won't help.

Check for the ones starting with 117.
If the suspicious contents are cached, he may verify it with my other post's contents.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Cutting a cone with a plane

You can got to various sites that will tell the IP that you came in here with.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Cutting a cone with a plane

Ah, yes, email.

Yesterday I did not check.

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"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Cutting a cone with a plane

Okay, I will send that one to MIF.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.