What is the surface area in square centimeters of a cone with a diameter of 12 ft and a slant height of 14 ft use 3.14 for pi round to the nearest tenth
To find the surface area of a cone, we need to find the area of the base and the lateral area.
The formula for the lateral area of a cone is given by:
Lateral Area = π × r × L, where r is the radius of the base and L is the slant height.
First, let's find the radius (r) using the given diameter of 12 ft.
The radius is equal to half of the diameter:
r = 12 ft / 2 = 6 ft
Next, let's calculate the lateral area:
Lateral Area = π × 6 ft × 14 ft = 264 ft² (rounded to the nearest tenth)
The formula for the surface area of a cone is given by:
Surface Area = Lateral Area + Base Area
The base area of a cone is given by:
Base Area = π × r²
Since the radius is 6 ft, the base area is:
Base Area = π × (6 ft)² = 36π ft²
Thus, the surface area is:
Surface Area = Lateral Area + Base Area
Surface Area = 264 ft² + 36π ft² = 264 ft² + 36 × 3.14 ft² ≈ 264 ft² + 113.04 ft² = 377.04 ft² (rounded to the nearest tenth)
Therefore, the surface area of the cone is approximately 377.04 square feet.