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To calculate the surface area of the cone, we need to find the lateral surface area and the base area first.
The lateral surface area of a cone is given by the formula: LSA = π * r * l, where r is the radius and l is the slant height.
Substituting the given values into the formula, we get: LSA = 3.14 * 6 cm * 18 cm = 339.12 square centimeters.
The base area of a cone is given by the formula: BA = π * r^2.
Substituting the given value into the formula, we get: BA = 3.14 * (6 cm)^2 = 113.04 square centimeters.
The total surface area of the cone is then found by adding the lateral surface area to the base area: TSA = LSA + BA = 339.12 square centimeters + 113.04 square centimeters = 452.16 square centimeters.
Therefore, the surface area of the spyglass is 452.16 square centimeters.