To find the surface area of the silo, we need to find the lateral surface area of the cylinder as well as the areas of the top and bottom surfaces.
1. Lateral Surface Area:
The formula for finding the lateral surface area of a cylinder is 2πrh, where r is the radius and h is the height. Since the diameter is 72 inches, the radius is half of that, which is 36 inches. We need to convert the height from feet to inches, so 22 feet is equal to 264 inches. Then, plug these values into the formula:
Lateral Surface Area = 2 * 3.14 * 36 * 264 = 84,499.52 square inches.
2. Top and Bottom Surfaces:
The formula to find the area of a circle is πr^2, where r is the radius. Using the formula with the radius of 36 inches:
Area of Top and Bottom Surfaces = 2 * 3.14 * 36^2 = 8,152.32 square inches.
3. Total Surface Area:
Add the lateral surface area to the top and bottom surfaces' area:
Total Surface Area = 84,499.52 + 8,152.32 = 92,651.84 square inches.
Now, convert square inches to square feet by dividing by 144 (1 square foot = 144 square inches):
92,651.84 / 144 = 644.74 square feet.
Therefore, the surface area of the silo is 644.74 ft^2.
None of the given responses are correct.
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
471.0 ft.2
471.0 ft. squared
13,112.64 ft.2
13,112.64 ft. squared
1,055.04 ft.2
1,055.04 ft. squared
414.48 ft.2
1 answer