Six congruent circles form a ring with each circle externally tangent to two circles adjacent to it. All circles are internally tangent to a circle \(C\) with radius 30. Let \(K\) be the area of the region inside circle \(C\) and outside of the six circles in the ring. Find \(\lfloor K \rfloor.\)

(第二十三届AIME1 2005 第1题)