Stretched Cube problem

[PatriotAlanis]

this is the only problem that has driven me crazy this year, please help y'all.

Im assuming everyone knows what im referring to.

[stupidityismygam]

sadly i dont....any reference tests?

or i guess if it isnt geometry post the problem

[PatriotAlanis]

Consider a cube that can be stretched in one
direction while the square cross section decreases in such
a way as to keep the volume constant. What is the length
to side ratio if the final area divided by the original
area of the cube equals the natural logarithm of pi?

[LeoG]

(X-1)^3 +2=3*(X-1)*whatever they give you for the last number

solve for X then...

1/(X-1)^3

[PatriotAlanis]

[LeoG]

It was vaguely explained to me. I just got the shortcuts for em and there they are for whoever comes across that problem. Anyone care to explain then go ahead lol

[Kurt]

I know how to solve it - somewhat. I don't know an explicit solution for the ratio, but I know what function I need to enter into my equation solver to get the solution (if that makes sense, lol). I can't see how to write it explicitly.

Let [unparseable or potentially dangerous latex formula]

We know the final surface area over original, which is:

[unparseable or potentially dangerous latex formula].

However, since we know that [unparseable or potentially dangerous latex formula], then [unparseable or potentially dangerous latex formula], and so:
(and now making the assignment [unparseable or potentially dangerous latex formula],

[unparseable or potentially dangerous latex formula].

^^^ That right there is what I would put in my calculator. I've tried putting it in a more explicit form with no luck.

(Oh, and sorry for the messed up latex...I don't know very much about latex at all, and I can't figure out how to correct it to make it bigger and more legible. Ask me if anything still needs clarification.)

[AuSmith]

[Kurt]

I actually just noticed that. :P With so many {'s and ('s, I guess I forgot one.

Oh, and yeah I did mean 2/3 instead...oops, I'll go edit that in. :) Thanks.

[PatriotAlanis]

When solving the above equations, several solutions exist (as expected). How do you know, without looking at the answer key, which one is correct?

[Kurt]

Actually, looking back I made another typo. There shouldn't be an [unparseable or potentially dangerous latex formula] in the numerator...only an [unparseable or potentially dangerous latex formula].

So the solution is:

[unparseable or potentially dangerous latex formula]

You can eliminate solutions for being non-physical. Obviously the negative solutions can be eliminated...the ratio of side lengths can't be negative. You can also eliminate answer choices less than one, since [unparseable or potentially dangerous latex formula] (the cube is being stretched according to the problem).

edit: Finally found the latex to make it all bigger. :)

[PatriotAlanis]

Thanks Kurt!