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
To find the surface area of the silo, we need to find the area of the cylinder's lateral surface, the area of the top circle (ceiling), and the area of the bottom circle (floor), and then add them together.
1. The lateral surface area of a cylinder can be calculated using the formula:
Lateral Surface Area = 2πr * h
where r is the radius of the cylinder and h is the height of the cylinder. Since the diameter is given, we need to first convert it to radius by dividing by 2:
Radius = 72 inches / 2 = 36 inches
Now, converting the radius to feet:
Radius = 36 inches * (1 foot / 12 inches) = 3 feet
Lateral Surface Area = 2 * 3.14 * 3 * 22 = 396.24 ft²
2. The area of the top circle (ceiling) can be calculated using the formula:
Top Circle Area = πr²
Top Circle Area = 3.14 * 3² = 28.26 ft²
3. The area of the bottom circle (floor) will also be the same as the top circle:
Bottom Circle Area = Top Circle Area = 28.26 ft²
Now, we can calculate the total surface area by adding all the areas together:
Total Surface Area = Lateral Surface Area + Top Circle Area + Bottom Circle Area = 396.24 ft² + 28.26 ft² + 28.26 ft² = 452.76 ft²
Therefore, the surface area of the silo is 452.76 ft². Answer choices 414.48 ft.2 and 414.48 ft. squared are both incorrect. 471.0 ft.2 and 471.0 ft. squared are also incorrect. 1,055.04 ft.2 and 1,055.04 ft. squared are incorrect. 13,112.64 ft.2 is also incorrect.