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The total surface area of a solid right circular cylinder is 231 cm². its curved surface is 2/3rd of the total surface. find the radius of the base and

Total surface area of a solid circular cylinder = 231 cm² Its curved surface area = 2πrh Total surface area = 2πrh + 2πr² 2πrh + 2πr² = 231............. - (1) Curved surface area is 2/3rd of the total surface area Therefore, 2πrh = 2/3 * 231 2πrh = 154................ - (2) Substituting value of 2πrh from equation (2) into equation (1), we get, 154 + 2πr² = 231 2πr² = 231 - 154 2πr² = 77 2 * 22/7 * r² = 77 44/7 r² = 77 r² = 77 / 44/7 r² = 77 * 7 / 44 r² = 539 / 44 r² = 12.25 r = √12.25 r = 3.5 cm Substituting r's value in equation (2), we get, 2 * 22/7 * 3.5 * h = 154 (44 * 3.5)h / 7= 154 22h = 154 h = 154 / 22 h = 7 cm Therefore, radius = 3.5 cm and height = 7 cm.