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, and \( l \) is the slant height.
- Find the radius: The diameter of the cone is 16 inches, so the radius \( r \) is:
\[ r = \frac{\text{diameter}}{2} = \frac{16}{2} = 8 \text{ inches} \]
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Given slant height: The slant height \( l \) is given as 9 inches.
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Calculate the surface area: Now we can substitute the values into the surface area formula:
\[ \text{Surface Area} = \pi r^2 + \pi r l \]
First, calculate \( \pi r^2 \):
\[ \pi r^2 = 3.14 \times (8^2) = 3.14 \times 64 = 200.96 \text{ square inches} \]
Next, calculate \( \pi r l \):
\[ \pi r l = 3.14 \times 8 \times 9 = 3.14 \times 72 = 226.08 \text{ square inches} \]
- Add both areas:
\[ \text{Surface Area} = 200.96 + 226.08 = 427.04 \text{ square inches} \]
Thus, the surface area of the cone is:
\[ \boxed{427.04} \text{ square inches} \]