What is the surface area of the lateral face of a cone with a radius of 27 feet and a slant height of 40 feet?
a. 4072 ft² b. 2375 ft²
c. 4411 ft² d. 3393 ft²
The surface area of the lateral face of a cone can be found using the formula:
Lateral surface area = π * r * l
where r is the radius and l is the slant height of the cone.
Plugging in the given values, the lateral surface area is:
Lateral surface area = π * 27 ft * 40 ft
Using an approximation of π = 3.14, the lateral surface area is:
Lateral surface area ≈ 3.14 * 27 ft * 40 ft
Lateral surface area ≈ 3384.24 ft²
Rounded to the nearest whole number, the lateral surface area is approximately 3384 ft².
Therefore, the correct answer is d. 3393 ft².