cubes...

[wviperw]

Why does the cube hold the most out of all the rectangular solids? I know this is true by common sense, and by pluggin in a few numbers, but what is the math formula or whatever. It's Calculus, right? I haven't learned calc yet, but for my pre-cal class I need to "explain some of the underlying math principles for the change in volume that occurs when shapes and dimensions are varied" And I am doing the cube.

I have no experience with Calc., all I know is that it has to do with integrals and differentiating or somthing like that... ??

Can anybody help, or give me website that would help?

 

[BA]

change=differential. Do you mean for having a constant sum of length, height, and width, the cube has the greatest volume?

 

[Spuffin]

The cube holds the most because as any side increases all other sides must increase respectively.

my 2¢

 

I think the fact you're trying to get is that the cube has the greatest volume for a set surface area, surface area being set by a certain perimeter.

 

[wviperw]

oops, forgot to mention that they all must have the same surface area.

 

[SexEPid]

I am in Pre-Calc, haven't gone over this yet...sounds like a challange, can't wait!

Pid, TYRP

 

[wviperw]

yea, I'm in Pre-Cal too. Check the "M&M Container" thread that I started awhile ago. This question is kinda related to that...

 

[jhu]

of course if you weren't working with rectangular solids, a sphere would have the greatest volume:surface area ratio

 

[wviperw]

yea I know, but don't even think about the sphere. Anybody know of the equation yet?

 

[AvesPKS]

Ahh, Pre-Calc...those were the days...DiffEq's not too bad, though...LaPlace transforms, Power series...