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.

Answer 1

First, we need to convert the diameter from inches to feet by dividing by 12 since 1 foot is equal to 12 inches.
72 inches / 12 = 6 feet

Now we can calculate the radius of the cylinder:
Radius = Diameter / 2 = 6 feet / 2 = 3 feet

Next, we can calculate the surface area of the cylinder:
Surface area of the side = 2 * π * radius * height
Surface area of the side = 2 * 3.14 * 3 feet * 22 feet
Surface area of the side = 6.28 * 3 feet * 22 feet
Surface area of the side = 411.84 square feet

Now we need to calculate the surface area of the ceiling and floor, which are both circles:
Surface area of the ceiling and floor = 2 * π * radius^2
Surface area of the ceiling and floor = 2 * 3.14 * (3 feet)^2
Surface area of the ceiling and floor = 2 * 3.14 * 9 square feet
Surface area of the ceiling and floor = 56.52 square feet

Finally, we can add the surface area of the side, ceiling, and floor to get the total surface area of the silo:
Total surface area = Surface area of the side + Surface area of the ceiling and floor
Total surface area = 411.84 square feet + 56.52 square feet
Total surface area = 468.36 square feet

Therefore, the surface area of the silo, including its ceiling and floor, is 468.36 square feet.