1. **State the problem:** We are given a cylinder with a top face area of $14\pi$ cm² and a curved surface area of $29\pi$ cm². We need to find the total surface area of the cylinder in terms of $\pi$. 2. **Recall the formulas:** - The area of the top (or bottom) face of a cylinder is $A_{\text{circle}} = \pi r^2$. - The curved surface area (lateral surface area) is $A_{\text{curved}} = 2\pi r h$. - The total surface area of a cylinder is $A_{\text{total}} = 2 \times A_{\text{circle}} + A_{\text{curved}}$ because it has two circular faces (top and bottom) plus the curved surface. 3. **Identify given values:** - Top face area: $\pi r^2 = 14\pi$ so $r^2 = 14$. - Curved surface area: $2\pi r h = 29\pi$ so $2 r h = 29$. 4. **Calculate total surface area:** $$ A_{\text{total}} = 2 \times 14\pi + 29\pi = 28\pi + 29\pi = 57\pi $$ 5. **Answer:** The total surface area of the cylinder is $\boxed{57\pi}$ cm².