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sagoyal

Here we see that the right circle has equal area because the segments on the outer edges are skinner yet longer which means that they occupy the same area as the bigger shorter sectors in the center.

sreyahalder

If we choose r uniformly, we break the left circle into rings that are equally spaced, since every r value is equally likely to occur. If we choose r with a square root function, we choose r values that are more bunched up towards the edge of the circle.