Final Answer:
The surface area of the cone in terms of π is 396π ft², thus the correct option is A.
Step-by-step explanation:
The formula for finding the surface area of a cone involves the addition of two components: the area of the base (πr²) and the lateral surface area (πrℓ), where r is the radius of the base and ℓ is the slant height of the cone (option A).
The lateral surface area of a cone is given by the formula Lateral Surface Area} = πrℓ. However, the slant height (ℓ) can be calculated using the Pythagorean theorem, where ℓ² = r² + h², with h as the height of the cone and r as the radius of the base.
To find the lateral surface area, it's crucial to know the radius (r) and height (h) of the cone. Assuming these measurements are provided, we calculate the slant height (ℓ) using ℓ = √(r² + h²). Then, the lateral surface area can be calculated as Lateral Surface Area} = πrℓ .
Adding the base area (πr²) to the lateral surface area provides the total surface area of the cone, given by Surface Area = Lateral Surface Area + Base Area = πrℓ + πr² . If the given measurements for the cone align with the calculations, the total surface area can be evaluated, resulting in the correct value expressed in terms of π. Hence, the surface area of 396π ft² is the appropriate solution among the options provided.