math help: Geometry Puzzle:

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Geometry Puzzle:

I am trying to figure out if there is a physical geometrical object which has the following properties:

Either:

A) as SA decreases, the SA/V ratio remains constant

OR

B) as SA decreases, the SA/V ratio increases

Clearly a sphere fails:

SA~=4*pi*R^2
V~=4/3*pi*R^3

SA/V=3/R (Not constant, Not increasing when R decreases)

Are there shapes that fit either A or B?

R=Radius
SA=Surface area
V=Volume

Thanks!

This open post was written 1 month, 1 week ago | V/U/S: 79, 2, 1 | Edit Post | Leave a reply | Report Post

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fractal.scatter 288 #
An Unknown Location | 1 month, 1 week ago (19 minutes after post)

Try a higher dimension.

howno #
An Unknown Location | 1 month, 1 week ago (25 minutes after post)

Yeah I think it could be solvable in higher order dimensions, but I’m trying to figure out a solution in 3 space.

Alternatively,

I can’t come up with a simple proof which refutes the possibility, but would be interested if someone has one!

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