The ratio of curved surface area of a right circular cylinder to the total area of its two bases is 2:1. If the total surface area of cylinder is 23100 square cm then what is the volume of cylinder?

Curved surface area = 2πrh, total base area = 2πr². Given 2πrh : 2πr² = 2:1, so h : r = 2:1, meaning h = 2r. Total surface area = 2πrh + 2πr² = 2πr(2r) + 2πr² = 4πr² + 2πr² = 6πr² = 23100. So πr² = 23100/6 = 3850. Volume = πr²h = πr²(2r) = 2πr²×r = 2×3850×√(3850/π). Wait, let me solve directly. 6πr² = 23100, r² = 23100/(6π) = 3850/π. r = √(3850/π). h = 2r. Volume = πr²h = π×(3850/π)×2√(3850/π) = 3850×2√(3850/π) = 7700×√(3850/π). Using π ≈ 3.1416: √(3850/3.1416) ≈ √1225.54 ≈ 35.01. Volume ≈ 7700×35.01 ≈ 269577. Closest to 269500. Yes, option B.