Question 1
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 $K.$)