To find the surface area of the spyglass in the shape of a cone, we need to calculate both the lateral surface area and the base area of the cone.
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Lateral Surface Area (LSA): The formula for the lateral surface area of a cone is:
\[ LSA = \pi r l \] where \( r \) is the radius and \( l \) is the slant height. Given \( r = 6 \) cm and \( l = 18 \) cm, we can substitute these values into the formula:
\[ LSA = 3.14 \times 6 \times 18 \]
\[ LSA = 3.14 \times 108 = 339.12 \text{ square centimeters} \]
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Base Area (BA): The formula for the area of the base of a cone (which is a circle) is:
\[ BA = \pi r^2 \]
Substituting \( r = 6 \) cm:
\[ BA = 3.14 \times 6^2 = 3.14 \times 36 = 113.04 \text{ square centimeters} \]
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Total Surface Area (TSA): The total surface area of the cone is the sum of the lateral surface area and the base area:
\[ TSA = LSA + BA \] \[ TSA = 339.12 + 113.04 = 452.16 \text{ square centimeters} \]
Thus, the surface area of the spyglass is 452.16 square centimeters.