A particular cylindrical bucket has a height of 36.0 cm, and the radius of its circular cross-section is 15 cm. The bucket is empty, aside from containing air. The bucket is then inverted so that its open end is down and, being careful not to lose any of the air trapped inside, the bucket is lowered below the surface of a fresh-water lake so the water-air interface in the bucket is 20.0 m below the surface of the lake. To keep the calculations simple, use g = 10 m/s^2, atmospheric pressure = 1 x 10^5 Pa, and the density of water as 1000 kg/m^3.

If the temperature is the same at the surface of the lake and at a depth of 20.0m below the surface , what is the height of the cylinder of air in the bucket when the bucket is at a depth of 20.0m below the surface of the lake?