Lucas needs to determine the surface area of a silo that is in the shape of a cylinder, including its ceiling and floor. If the height is 22 feet and the diameter is 72 inches, what is the silo’s surface area? Use 3.14 for π .(1 point) Responses 414.48 ft.2 414.48 ft. squared 1,055.04 ft.2 1,055.04 ft. squared 471.0 ft.2 471.0 ft. squared 13,112.64 ft.2 13,112.64 ft. squared
The first step is to convert the diameter from inches to feet by dividing 72 inches by 12:
72 inches / 12 = 6 feet
Next, we calculate the radius of the cylinder by dividing the diameter by 2:
6 feet / 2 = 3 feet
Now, we can calculate the surface area of the lateral side of the cylinder using the formula: 2πrh, where r is the radius and h is the height:
2 x 3.14 x 3 ft x 22 ft = 396.24 ft²
The surface area of the two circular bases can be calculated using the formula: πr², where r is the radius:
2 x 3.14 x (3 ft)² = 56.52 ft²
Adding the surface area of the lateral side and the two bases gives us the total surface area of the silo:
396.24 ft² + 56.52 ft² + 56.52 ft² = 509.28 ft²
Therefore, the surface area of the silo, including its ceiling and floor, is 509.28 ft². So the closest option would be rounded to 471.0 ft.².