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 it by 12 (since 1 foot is equal to 12 inches):
72 inches / 12 = 6 feet

Now, we can calculate the radius of the cylinder by dividing the diameter by 2:
Radius = 6 feet / 2 = 3 feet

Next, we calculate the lateral surface area of the cylinder using the formula:
Lateral Surface Area = 2πrh
where r is the radius and h is the height of the cylinder

Lateral Surface Area = 2 * 3.14 * 3 feet * 22 feet
Lateral Surface Area = 6.28 * 3 feet * 22 feet
Lateral Surface Area = 414.48 square feet

Next, we calculate the area of the top and bottom circles (ceiling and floor) using the formula:
Top and Bottom Area = 2πr^2
where r is the radius of the circle

Top and Bottom Area = 2 * 3.14 * (3 feet)^2
Top and Bottom Area = 2 * 3.14 * 9 square feet
Top and Bottom Area = 56.52 square feet

Finally, we calculate the total surface area by adding the lateral surface area with the area of the top and bottom circles:
Total Surface Area = Lateral Surface Area + Top and Bottom Area
Total Surface Area = 414.48 square feet + 56.52 square feet
Total Surface Area = 471 square feet

Therefore, the surface area of the silo, including its ceiling and floor, is 471 square feet.