To find the surface area of the cone-shaped spyglass, we need to calculate both the lateral surface area and the base area of the cone.
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Lateral Surface Area (A_l): The formula for the lateral surface area of a cone is given by:
\[ A_l = \pi r l \]
where:
- \( r \) is the radius of the base,
- \( l \) is the slant height.
Given:
- \( r = 6 \) cm,
- \( l = 18 \) cm,
- \( \pi \approx 3.14 \).
Now, plug in the values:
\[ A_l = 3.14 \times 6 \times 18 \] \[ A_l = 3.14 \times 108 = 339.12 \text{ square centimeters} \]
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Base Area (A_b): The formula for the area of the base (which is a circle) is:
\[ A_b = \pi r^2 \]
Using the same radius:
\[ A_b = 3.14 \times (6^2) = 3.14 \times 36 = 113.04 \text{ square centimeters} \]
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Total Surface Area (A): The total surface area of the cone is the sum of the lateral surface area and the base area:
\[ A = A_l + A_b \] \[ A = 339.12 + 113.04 = 452.16 \text{ square centimeters} \]
Thus, the total surface area of the spyglass is 452.16 square centimeters.
The correct answer is:
452.16 square centimeters.
1 answer