Six congruent circles form a ring with each circle externally tangent to the two circles adjacent to it. All six circles are internally tangent to a circle \mathcal{C} with radius 30. Let K be the area of the region inside \mathcal{C} and outside all of the six circles in the ring. Find \lfloor K\rfloor. (The notation \lfloor K\rfloor denotes the greatest integer that is less than or equal to K.)