Prove this please

[Nelis Parts]

Hi!

I know this is pretty easy for you big math hot shots, but I really need
it proven as fast as possbile.

You have a box and inside you can exactly place four balls. And now you
have to prove that the volume ratio is 3:2!

I hope that someone will help me with this!

[Zdislav V. Kovarik]

In article <3845563A...@swipnet.se>,
Nelis Parts <nelis...@swipnet.se> wrote:
:Hi!

Why? It's not even a problem, just hastily copied bits and pieces of what
might have been either an elementary problem or a hard combinatorial
puzzle. (The way I reconstructed the problem, I got not 3:2 but 2*pi/3.
The balls are the same size, the box is a cube that holds one ball
tightly, and the balls are placed in the box one at a time, each
time removing the previous ball if it was in. And it is the ratio of the
combined volume of the balls to the volume of the box.:-)=

Is it for exams, practice, competition?

And: the "big math hot shots" cliche is so tired that it deserves to be
retired.

Cheers, ZVK(Slavek)

[William L. Bahn]

What is a "volume ratio"? Do you mean the volume of the box to the volume of
the balls?

What do you mean by "exactly place"?

Is the "box" a rectangular solid?

Are the balls all the same size?

Nelis Parts wrote in message <3845563A...@swipnet.se>...

[s_d...@my-deja.com]

Can't prove it because it depends on the size/shape of the box...
I'm assuming you just lost your bet buddy... However, if you
specified the shape of the box... ;-)

-slew

In article <3845563A...@swipnet.se>,
Nelis Parts <nelis...@swipnet.se> wrote:

> Hi!
>
> I know this is pretty easy for you big math hot shots, but I really
need
> it proven as fast as possbile.
>
> You have a box and inside you can exactly place four balls. And now
you
> have to prove that the volume ratio is 3:2!
>
> I hope that someone will help me with this!
>
>

Sent via Deja.com http://www.deja.com/
Before you buy.

[NFN NMI L.]

<<You have a box and inside you can exactly place four balls. And now you
have to prove that the volume ratio is 3:2!>>

Assuming that the balls are packed as tightly as possible (tetrahedron)? Or
what? Get lost.

S. "Morons abound" L.

[Chris Ferrante]

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Nelis Parts <nelis...@swipnet.se> wrote in message
news:3845563A...@swipnet.se...

> Hi!
>
> I know this is pretty easy for you big math hot shots, but I really need
> it proven as fast as possbile.
>

> You have a box and inside you can exactly place four balls. And now you
> have to prove that the volume ratio is 3:2!
>

[Chris Ferrante]

Quite sorry about the other post, I hit send accidentally!!

Well this problem is interesting, but it lacks information. Mr. Bahn
pointed that out to you. I would suspect that the box is rectangular and
the balls are the same size, so I will go with that. The volume of the box
is either V = xyz, V = x^2*y or V = x^3 (a cube box, possible). Well, the
volume of the balls can be expressed as V (all of them) = 16/3 * pi * r^3.
Well, the next step is to relate some of these many variables together so
that, hopefully you can put things in terms of one of them, then the ratio
would become apparent. Otherwise, you need to prove that V(box)/V(spheres)
= 3/2 = xyz/((16/3* pi * r^3)) or whatever box formula is correct and prove
from that. I can't do it though, I think there's too many variables here.
Maybe I'm wrong, any suggestions people of sci.math????

Chris

[Mike Lugo]

The type of box isn't clear, but I'm thinking cylindrical, like a tennis
ball can. Assuming the balls have radius R, and the can has radius R and
height 8R:
the total volume of the balls is 4 * ((4/3) * PI * R^3) = 16/3*PI*R^3
the volume of the can is (PI*R^2)* 8
and the ratio between these is 3:2.

NFN NMI L. <stl...@aol.com> wrote in message
news:19991201200804...@ng-fo1.aol.com...

> <<You have a box and inside you can exactly place four balls. And now you
> have to prove that the volume ratio is 3:2!>>
>

[Nathaniel Silver]

Good job, Mike.
Your post not only solves the problem
but also makes the rest of the posters
look like defensive hotshots.

Mike Lugo wrote in message ...

>The type of box isn't clear, but I'm thinking cylindrical,
>like a tennis ball can. Assuming the balls have radius R,
>and the can has radius R and height 8R:
>the total volume of the balls is 4 * ((4/3) * PI * R^3) = 16/3*PI*R^3
>the volume of the can is (PI*R^2)* 8
>and the ratio between these is 3:2.

>NFN NMI L. <stl...@aol.com> wrote

>>You have a box and inside you can exactly place four balls.

>>And now you have to prove that the volume ratio is 3:2.