To find the surface area of a cone, we need to calculate the lateral surface area and the area of the base separately.
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Lateral Surface Area: The formula for the lateral surface area (A_l) of a cone is given by: \[ A_l = \pi r l \] where \( r \) is the radius and \( l \) is the slant height.
Given:
- \( r = 6 \) cm
- \( l = 18 \) cm
- Using \( \pi = 3.14 \)
Now substituting the values into the formula: \[ A_l = 3.14 \times 6 \times 18 \]
Now calculating it step-by-step:
- \( 6 \times 18 = 108 \)
- \( 3.14 \times 108 = 339.12 \) square centimeters
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Base Area: The area of the base (A_b) of the cone can be found using the formula: \[ A_b = \pi r^2 \] Substituting the values: \[ A_b = 3.14 \times 6^2 = 3.14 \times 36 \] Calculating it:
- \( 3.14 \times 36 = 113.04 \) square centimeters
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Total Surface Area: Finally, the total surface area (A) of the cone is the sum of the lateral area and the base area: \[ A = A_l + A_b = 339.12 + 113.04 = 452.16 \]
Thus, the surface area of the spyglass is 452.16 square centimeters.