A solid cylinder has a total surface area of 231 sq. cm. If its curved surface area is (\frac{2}{3}) of the total surface area, then the volume of the cylinder is

Total surface area = 231 cm², curved surface area = (2/3) × 231 = 154 cm². This means the area of the two circular bases is 231 - 154 = 77 cm². So 2πr² = 77, giving r² = 77/(2π). Curved surface area = 2πrh = 154. Substituting r, we get h = 154/(2πr). Volume = πr²h = πr² × 154/(2πr) = 77r. Using r = √(77/(2π)), volume ≈ 77 × 3.5 = 269.5 cm³.