To find the surface area of the cone-shaped spyglass, we will calculate both the lateral surface area and the base area.
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Lateral Surface Area (A_later) of a cone is given by the formula: \[ A_{lateral} = \pi r l \] where:
- \( r = 6 \) cm (radius)
- \( l = 18 \) cm (slant height)
Substituting the values: \[ A_{lateral} = 3.14 \times 6 \times 18 \] \[ A_{lateral} = 3.14 \times 108 = 339.12 \text{ square centimeters} \]
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Base Area (A_base) of the cone is given by the formula: \[ A_{base} = \pi r^2 \] Substituting the values: \[ A_{base} = 3.14 \times 6^2 = 3.14 \times 36 = 113.04 \text{ square centimeters} \]
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Total Surface Area (A_total) of the cone is the sum of the lateral surface area and the base area: \[ A_{total} = A_{lateral} + A_{base} \] \[ A_{total} = 339.12 + 113.04 = 452.16 \text{ square centimeters} \]
Therefore, the total surface area of the spyglass is 452.16 square centimeters.
The correct response is: 452.16 square centimeters.