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 PI.

Question

A. 471.0 ft. squared
B. 414.48 ft. squared
C. 1,055.04 ft. squared
D. 13,112.64 ft. squared

Answer 1

First, we need to convert the diameter from inches to feet by dividing by 12 (since 1 foot = 12 inches):

72 inches / 12 = 6 feet

Now, we can find the radius of the cylinder by dividing the diameter by 2:

6 feet / 2 = 3 feet

Next, we calculate the lateral surface area of the cylinder using the formula 2 * PI * radius * height:

2 * 3.14 * 3 feet * 22 feet = 13,112.64 ft. squared

The surface area of the ceiling and floor can be found using the formula PI * radius^2 for each, since they are both circles:

2 * 3.14 * 3 feet^2 = 56.52 ft. squared

Adding the lateral surface area to the surface area of the ceiling and floor, we get:

13,112.64 ft. squared + 56.52 ft. squared = 13,169.16 ft. squared

Therefore, the correct answer is D. 13,112.64 ft. squared.