Final answer:
The volume of the cylinder is approximately 77.21cm³.
Step-by-step explanation:
Given that the total surface area of the cylinder is 462cm² and the curved surface area is one-third of the total surface area, we can set up the following equation:
CSA = 1/3 * TSA
CSA = 1/3 * 462cm²
CSA = 154cm²
The curved surface area of a cylinder is given by the formula CSA = 2 * π * r * h, where r is the radius and h is the height. Since CSA = 154cm², we can solve for the radius:
154 = 2 * π * r * h
154 = 2 * 3.142 * r * h
154 = 6.284 * r * h
r * h = 24.54
Now, we can calculate the volume of the cylinder using the formula V = π * r² * h:
V = 3.142 * r² * h
V = 3.142 * (24.54/h) * h
V = 3.142 * 24.54
V ≈ 77.21cm³