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
1,356.48 square centimeters
1,356.48 square centimeters
339.12 square centimeters
339.12 square centimeters
452.16 square centimeters
452.16 square centimeters
197.82 square centimeters
To find the surface area of the spyglass, we need to find the lateral surface area of the cone and the area of the base.
The lateral surface area of a cone can be found using the formula:
Lateral Surface Area = π * radius * slant height
Let's calculate the lateral surface area:
Lateral Surface Area = π * 6 cm * 18 cm = 339.12 square centimeters
The base of the cone is a circle, and the area of a circle can be found using the formula:
Area of Circle = π * radius^2
Let's calculate the area of the base:
Area of Base = π * (6 cm)^2 = π * 36 cm^2 = 113.04 square centimeters
The total surface area of the spyglass is the sum of the lateral surface area and the area of the base:
Surface Area = Lateral Surface Area + Area of Base
Surface Area = 339.12 square centimeters + 113.04 square centimeters = 452.16 square centimeters
Therefore, the correct answer is:
452.16 square centimeters