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 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
To calculate the surface area of the cone, we need to find the lateral surface area and the base area first.
The lateral surface area of a cone is given by the formula: LSA = π * r * l, where r is the radius and l is the slant height.
Substituting the given values into the formula, we get: LSA = 3.14 * 6 cm * 18 cm = 339.12 square centimeters.
The base area of a cone is given by the formula: BA = π * r^2.
Substituting the given value into the formula, we get: BA = 3.14 * (6 cm)^2 = 113.04 square centimeters.
The total surface area of the cone is then found by adding the lateral surface area to the base area: TSA = LSA + BA = 339.12 square centimeters + 113.04 square centimeters = 452.16 square centimeters.
Therefore, the surface area of the spyglass is 452.16 square centimeters.