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 of the base,
- \( l \) is the slant height.
In this case:
- \( r = 6 \) cm,
- \( l = 18 \) cm,
- \( \pi \) is given as 3.14.
Now, substituting the values into the formula:
- Calculate the lateral surface area:
\[ \text{Lateral Surface Area} = \pi r l = 3.14 \times 6 \times 18 \]
Calculating this:
\[ = 3.14 \times 6 = 18.84 \] \[ = 18.84 \times 18 = 338.88 \text{ cm}^2 \]
- Calculate the base area:
\[ \text{Base Area} = \pi r^2 = 3.14 \times (6)^2 = 3.14 \times 36 \]
Calculating this:
\[ = 3.14 \times 36 = 113.04 \text{ cm}^2 \]
- Finally, add the lateral surface area and the base area to find the total surface area:
\[ \text{Total Surface Area} = \text{Lateral Surface Area} + \text{Base Area} = 338.88 + 113.04 = 451.92 \text{ cm}^2 \]
Thus, the surface area of the spyglass is approximately:
\[ \text{Surface Area} \approx 451.92 \text{ cm}^2 \]