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If you take A=pi*r^2 and change it to A=pi*r^3 (and if there's a formula for transition from 2D to 3D), then haven't you just turned a circle into a sphere? Or am I missing something here?

Actually, πr^3 gives you the volume of a cylinder that has a height equaling its radius (since the equation's πhr^2). For a sphere, the equation would be (4/3)πr^3 for volume and 4πr^2 for surface area.

That's not the formula for the area of a sphere. You're definitely missing something here. 

I'm talking about a literal transition. Like what if you drew a circle on a piece of paper, pinched the center and pulled out a sphere (Sci-fi/Fantasy realm, I know.)?

If you drew a circle on a piece of paper and cut it out, you'd just have a really thin cylinder...

Think about what you're doing with that equation. You're taking a 2D circle (πr^2) and creating a 3D shape by stacking it on top of itself to a height of r (πr^2 * r = πr^3). A sphere is not a stack of congruent circles.

I'm not talking about cutting it out. What if you were literally able to pull it out of the sheet, and it then taking on a 3D form?

That'd also be a thin cylinder. There's nothing on that 2-dimensional plane that says it's round, unless you shade it, unless that just makes it a cylinder with pencil marks.

Or unless you do that "Donald Duck in Mathemagic Land" thing and make it spin so fast it turns into a sphere, in which case, it would be a sphere according to the dimensions of the circle you drew, so you'd just have to use the circle calculator in Google.

Well, if you're using fictional Physics, I would not attempt to use equations in order to make sense of it.

Also, exponents do not work with non-square objects.

True.