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 1,055.04 ft.2 1,055.04 ft. squared 13,112.64 ft.2 13,112.64 ft. squared 414.48 ft.2 414.48 ft. squared 471.0 ft.2
To find the surface area of the silo, we need to calculate the lateral surface area of the cylinder (including the walls) as well as the surface area of the top and bottom (the ceiling and floor).
First, find the radius of the cylinder by dividing the diameter by 2:
Radius = 72 inches / 2 = 36 inches
Convert the height from feet to inches:
Height = 22 feet * 12 inches/foot = 264 inches
Calculate the lateral surface area of the cylinder using the formula:
Lateral Surface Area = 2πrh
Lateral Surface Area = 2 * 3.14 * 36 inches * 264 inches
Lateral Surface Area = 672.96 inches squared
Next, find the surface area of the top and bottom (the ceiling and floor) of the silo:
Top and Bottom Surface Area = 2πr^2
Top and Bottom Surface Area = 2 * 3.14 * (36 inches)^2
Top and Bottom Surface Area = 2 * 3.14 * 1296 square inches
Top and Bottom Surface Area = 8143.04 square inches
Add the lateral surface area and the top and bottom surface area to find the total surface area of the silo:
Total Surface Area = Lateral Surface Area + Top and Bottom Surface Area
Total Surface Area = 672.96 square inches + 8143.04 square inches
Total Surface Area = 8816 square inches
Convert the total surface area from square inches to square feet:
Total Surface Area = 8816 square inches / 144 square inches/square foot
Total Surface Area ≈ 61.22 square feet
Therefore, the surface area of the silo, including its ceiling and floor, is approximately 61.22 square feet.