Visualizing Pi (For example Pi×2, Pi²)

I understand that Pi is equal to the circumference of a circle divided by its radius.
So when I see Pi I think of it representing “circleness”.

Is there a visualization for Pi×2?
What about Pi²?

Does this question have an answer or am I thinking of this in a way that doesn’t make sense?

Pi is a dimensionless irrational number, a singular PSU in a ocean of PSUs.

Pi X 2 is super simple. This is one way to visualize it:
Each of the inner circles has a radius of one and the outer is two, so the idea is the smaller circle is half the circumference of the outer, which shows Pi times two, and there are two shown simply because exactly two fit perfectly in the doubled circle.

I’m not sure about Pi squared, though…

North of the artic circle, and more dynamically the earth’s circle of illumination, for every 1° increased latitude solar insolation, the sunlit area increases exponentially (πr^2). Which is why Earth’s Milankovitch Orbital cycles ultimately (almost, except during events of runaway CO2 and methane) control glaciation.