A cone has a curved surface area of 308 cm² and a slant height of 14 cm…

Step 1. The radius. $\pi r l = 308\ \text{cm}^2$ gives $\dfrac{22}{7} \times r \times 14\ \text{cm} = 308\ \text{cm}^2$. So $44r = 308\ \text{cm}$ and $r = 7\ \text{cm}$.

Step 2. The height. $h = \sqrt{l^2 - r^2} = \sqrt{14^2 - 7^2}\ \text{cm} = \sqrt{147}\ \text{cm} = 7\sqrt{3}\ \text{cm}$, which is $12.12\ \text{cm}$.

Step 3. The base. $\pi r^2 = \dfrac{22}{7} \times 49\ \text{cm}^2 = 154\ \text{cm}^2$.

Step 4. The total. $308\ \text{cm}^2 + 154\ \text{cm}^2 = 462\ \text{cm}^2$.