Maximize Evaporation -- Disk Wheel Humidifier

Calculus Level 4

A circular disk which is perpendicular to the water surface (partially submerged) keeps rotating slowly, as shown in the figure. What should be the height of the center of the disk from the surface of water, so that the area of the wet surface above the water is maximized?

In other words, find \(h\) such that the blue area above the water surface is maximized. And then, assume the radius of this disk as 3 units, and enter your answer to at least 3 decimal places.

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