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Ok, I need some math info and I

I'd like to know if you can determine the shape of a volume by the rate differences with which it fills up.

Let's say you are filling a ball with water. The ball is marked at regular intervals from the bottom to the top. If you want the rate at which the water level reaches each marked interval to remain constant, you must increase the amount and/or speed of the water entering as the water level approaches the "equator", right?

So, if you didn't already know you are filling a ball, is it possible to deduce that it IS a ball by the rate of increase if you know that you are maintaining the "interval constant"? I'm sure it is possible. I guess I'm just looking for a formula or something for how to figure out the shape. Maybe even just a specific topic that I can get a book on to figure it out.

I hope my question makes sense.

*think*this is the right section for my question, but I may be wrong. Is it physics? General math? I don't know.I'd like to know if you can determine the shape of a volume by the rate differences with which it fills up.

Let's say you are filling a ball with water. The ball is marked at regular intervals from the bottom to the top. If you want the rate at which the water level reaches each marked interval to remain constant, you must increase the amount and/or speed of the water entering as the water level approaches the "equator", right?

So, if you didn't already know you are filling a ball, is it possible to deduce that it IS a ball by the rate of increase if you know that you are maintaining the "interval constant"? I'm sure it is possible. I guess I'm just looking for a formula or something for how to figure out the shape. Maybe even just a specific topic that I can get a book on to figure it out.

I hope my question makes sense.

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