What are the lateral area and the surface area of the cone shown below? Round the answers to the nearest tenth. The figure is not drawn to scale.
14ft 27ft
To find the lateral area of a cone, we use the formula:
Lateral Area = πrℓ
where r is the radius of the base of the cone and ℓ is the slant height of the cone.
Given that the radius of the cone is 14ft and the slant height is 27ft, we can calculate the lateral area:
Lateral Area = π(14)(27) = 378π ≈ 1187.4 square feet
To find the surface area of a cone, we need to add the area of the base to the lateral area. The formula for the surface area of a cone is:
Surface Area = πr(r + ℓ)
where r is the radius of the base of the cone and ℓ is the slant height of the cone.
First, calculate the area of the base of the cone:
Base Area = πr^2 = π(14)^2 = 196π ≈ 615.8 square feet
Then, calculate the surface area:
Surface Area = 196π + 378π = 574π ≈ 1803.2 square feet
Therefore, the lateral area of the cone is approximately 1187.4 square feet and the surface area is approximately 1803.2 square feet.