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.
-
Lateral Surface Area of a cone is calculated using the formula: \[ \text{Lateral Surface Area} = \pi r l \] where \( r \) is the radius and \( l \) is the slant height.
-
Base Area of a cone is calculated using the formula: \[ \text{Base Area} = \pi r^2 \]
-
Total Surface Area is the sum of the lateral surface area and the base area: \[ \text{Total Surface Area} = \text{Lateral Surface Area} + \text{Base Area} \]
Given:
- Radius \( r = 6 \) cm
- Slant height \( l = 18 \) cm
- Use \( \pi = 3.14 \)
Step 1: Calculate Lateral Surface Area \[ \text{Lateral Surface Area} = 3.14 \times 6 \times 18 \] \[ = 3.14 \times 108 \] \[ = 339.12 \text{ square centimeters} \]
Step 2: Calculate Base Area \[ \text{Base Area} = 3.14 \times (6^2) = 3.14 \times 36 \] \[ = 113.04 \text{ square centimeters} \]
Step 3: Calculate Total Surface Area \[ \text{Total Surface Area} = 339.12 + 113.04 \] \[ = 452.16 \text{ square centimeters} \]
Thus, the surface area of the spyglass is 452.16 square centimeters.
The correct option is:
- 452.16 square centimeters