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

1 answer

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.