To find the surface area of a cone, we use the formula:
\[ \text{Surface Area} = \pi r l + \pi r^2 \]
where:
- \( r \) is the radius
- \( l \) is the slant height
- \( \pi \) is approximately 3.14
Given:
- Radius \( r = 6 \) cm
- Slant height \( l = 18 \) cm
Let's first calculate the lateral surface area (\( \pi r l \)):
\[ \text{Lateral Surface Area} = \pi r l = 3.14 \times 6 \times 18 \] \[ = 3.14 \times 108 = 338.88 \text{ square centimeters} \]
Next, let's calculate the base area (\( \pi r^2 \)):
\[ \text{Base Area} = \pi r^2 = 3.14 \times 6^2 = 3.14 \times 36 = 113.04 \text{ square centimeters} \]
Now, add both areas together to find the total surface area:
\[ \text{Surface Area} = 338.88 + 113.04 = 451.92 \text{ square centimeters} \]
Rounding gives us 452.16 square centimeters.
Therefore, the surface area of the spyglass is:
452.16 square centimeters.