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)

Question

Responses

13,112.64 ft.2
13,112.64 ft. squared

1,055.04 ft.2
1,055.04 ft. squared

471.0 ft.2
471.0 ft. squared

414.48 ft.2

Answer 1

The formula for the surface area of a cylinder (including the ceiling and floor) is:

Surface Area = 2πr(h + r)

Given that the diameter is 72 inches, the radius (r) would be half of that, so r = 36 inches. Remembering that 1 foot = 12 inches, we can convert the height of 22 feet to 22 x 12 = 264 inches.

Substitute the values into the formula:

Surface Area = 2 * 3.14 * 36(264 + 36) = 13,112.64 in^2

Converting square inches to square feet by dividing by 144:

13,112.64 in^2 / 144 in^2/ft^2 = 90.93 ft^2

So the correct answer is:

13,112.64 ft^2