To find the surface area of a cone, you 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.
We are given:
- The diameter of the cone is 16 inches, so the radius \( r \) is:
\[ r = \frac{16}{2} = 8 \text{ inches} \]
- The slant height \( l \) is 9 inches.
Now, we can plug in the values into the surface area formula.
- Calculate the area of the base:
\[ \text{Area of the base} = \pi r^2 = 3.14 \times (8^2) = 3.14 \times 64 = 200.96 \text{ square inches} \]
- Calculate the lateral surface area:
\[ \text{Lateral Surface Area} = \pi r l = 3.14 \times 8 \times 9 = 3.14 \times 72 = 226.08 \text{ square inches} \]
- Add the areas together to find the total surface area:
\[ \text{Total Surface Area} = \text{Area of the base} + \text{Lateral Surface Area} = 200.96 + 226.08 = 427.04 \text{ square inches} \]
Thus, the total surface area of the cone is 427.04 square inches.
The correct response is: 427.04 square inches.