A spyglass in the shape of a cone has a slant height of 18 centimeters and a radius of 6 centimeters. What is the surface area of the spyglass? Use 3.14 for pi.(1 point)

Question

Responses

197.82 square centimeters
197.82 square centimeters

452.16 square centimeters
452.16 square centimeters

339.12 square centimeters
339.12 square centimeters

1,356.48 square centimeters
1,356.48 square centimeters

Answer 1

To find the surface area of the cone-shaped spyglass, we will calculate both the lateral surface area and the base area.

1. Lateral Surface Area (A_later) of a cone is given by the formula: $$A_{lateral}=\pi rl$$ where:

   • $r=6$ cm (radius)
   • $l=18$ cm (slant height)

   Substituting the values: $$A_{lateral}=3.14\times 6\times 18$$ $$A_{lateral}=3.14\times 108=339.12\text{ square centimeters}$$

2. Base Area (A_base) of the cone is given by the formula: $$A_{base}=\pi r^2$$ Substituting the values: $$A_{base}=3.14\times 6^2=3.14\times 36=113.04\text{ square centimeters}$$

3. 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.