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) Responses 339.12 square centimeters 339.12 square centimeters 197.82 square centimeters 197.82 square centimeters 452.16 square centimeters 452.16 square centimeters 1,356.48 square centimeters

Question

GPT-4o mini · Answer

To find the surface area of a cone, we need to calculate the lateral surface area and the area of the base separately.

Lateral Surface Area: The formula for the lateral surface area (A_l) of a cone is given by: $A_{l} = π r l$ where $r$ is the radius and $l$ is the slant height.

Given:
- $r = 6$ cm
- $l = 18$ cm
- Using $π = 3.14$
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
Base Area: The area of the base (A_b) of the cone can be found using the formula: $A_{b} = π r^{2}$ Substituting the values: $A_{b} = 3.14 \times 6^{2} = 3.14 \times 36$ Calculating it:
- $3.14 \times 36 = 113.04$ square centimeters
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.