To find the surface area of a cone, you can use the formula:
\[ \text{Surface Area} = \pi r (r + l) \]
where \( r \) is the radius, \( l \) is the slant height, and \( \pi \) is approximately 3.14.
Given:
- Radius (\( r \)) = 6 cm
- Slant height (\( l \)) = 18 cm
Now, substituting the values into the formula:
\[ \text{Surface Area} = 3.14 \times 6 \times (6 + 18) \]
First, calculate \( (6 + 18) = 24 \).
Now substitute this into the formula:
\[ \text{Surface Area} = 3.14 \times 6 \times 24 \]
Calculating \( 3.14 \times 6 = 18.84 \).
Now, multiply by 24:
\[ \text{Surface Area} = 18.84 \times 24 = 452.16 \text{ square centimeters} \]
Thus, the surface area of the spyglass is 452.16 square centimeters.