To find the surface area of a cone, we need to calculate both the lateral surface area and the base area. The formula for the total surface area \( A \) of a cone is given by:
\[ A = \pi r l + \pi r^2 \]
where:
- \( r \) is the radius,
- \( l \) is the slant height.
First, we need to find the radius from the diameter. The diameter is given as 16, so:
\[ r = \frac{\text{diameter}}{2} = \frac{16}{2} = 8 \]
Next, we know the slant height \( l \) is given as 9.
Now we can calculate the two areas:
- Lateral Surface Area: \[ \text{Lateral Surface Area} = \pi r l = 3.14 \times 8 \times 9 \]
Calculating this step-by-step:
\[ 8 \times 9 = 72 \] \[ 3.14 \times 72 = 226.08 \]
Thus, the lateral surface area is \( 226.08 \).
- Base Area: \[ \text{Base Area} = \pi r^2 = 3.14 \times (8^2) \]
Calculating \( 8^2 \):
\[ 8^2 = 64 \]
Now multiplying:
\[ 3.14 \times 64 = 200.96 \]
Thus, the base area is \( 200.96 \).
- Total Surface Area: Adding the lateral surface area and the base area together:
\[ A = \text{Lateral Surface Area} + \text{Base Area} \] \[ A = 226.08 + 200.96 = 427.04 \]
Therefore, the total surface area of the cone is:
\[ \boxed{427.04} \]