To find the surface area of a cone, we can use the formula:
\[ \text{Surface Area} = \pi r^2 + \pi r l \]
where:
- \( r \) is the radius of the base of the cone,
- \( l \) is the slant height of the cone.
Given:
- Diameter = 16 inches, so radius \( r = \frac{16}{2} = 8 \) inches.
- Slant height \( l = 9 \) inches.
- Use \( \pi \approx 3.14 \).
Calculating the surface area:
- Area of the base:
\[ \text{Area of the base} = \pi r^2 = 3.14 \times (8^2) = 3.14 \times 64 = 200.96 \text{ square inches} \]
- Area of the lateral surface:
\[ \text{Lateral Surface Area} = \pi r l = 3.14 \times 8 \times 9 = 3.14 \times 72 = 226.08 \text{ square inches} \]
- Total surface area:
\[ \text{Total Surface Area} = \text{Area of the base} + \text{Lateral Surface Area} \] \[ \text{Total Surface Area} = 200.96 + 226.08 = 427.04 \text{ square inches} \]
Thus, the total surface area of the cone is \( \boxed{427.04} \) square inches.