The slant height of the cone is the hypotenuse of a right triangle formed by the slant height, the radius, and a line perpendicular to the slant height from the center of the base of the cone.
Using the Pythagorean theorem, we can find the height of the cone:
Height^2 + Radius^2 = Slant Height^2
Height^2 + 6^2 = 18^2
Height^2 + 36 = 324
Height^2 = 288
Height = sqrt(288)
Height ≈ 16.97 centimeters
The surface area of the spyglass can be found by adding the area of the base and the lateral surface area.
The area of the base is given by the formula for the area of a circle:
Base Area = π * Radius^2
Base Area = 3.14 * 6^2
Base Area = 3.14 * 36
Base Area ≈ 113.04 square centimeters
The lateral surface area is given by the formula for the lateral surface area of a cone:
Lateral Surface Area = π * Radius * Slant Height
Lateral Surface Area = 3.14 * 6 * 18
Lateral Surface Area = 339.12 square centimeters
Therefore, the surface area of the spyglass is:
Surface Area = Base Area + Lateral Surface Area
Surface Area ≈ 113.04 + 339.12
Surface Area ≈ 452.16 square centimeters
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 answer