Sonia cut a tree trunk in the shape of a cylinder. The length is 15 feet, and the diameter is 30 inches. Solve for the surface area, using 3.14 for π .(1 point) Responses 127.56 ft.2 127.56 ft. squared 274.75 ft.2 274.75 ft. squared 117.75 ft.2 117.75 ft. squared 2,826 ft.2
To find the surface area of a cylinder, you first need to find the lateral surface area (the curved surface) and then add the areas of the two circular bases.
1. Lateral Surface Area:
The formula for the lateral surface area of a cylinder is 2πrh, where r is the radius and h is the height. Since the diameter is given as 30 inches, the radius is half of that, which is 15 inches. However, the height is given as 15 feet, so you need to convert the height to inches. 15 feet is equal to 180 inches.
Lateral Surface Area = 2 * 3.14 * 15 * 180
Lateral Surface Area = 16956 square inches
2. Base Area:
The formula for the area of a circle is πr^2. Since the radius is 15 inches:
Base Area = 3.14 * 15^2
Base Area = 706.5 square inches (for each base)
3. Total Surface Area:
Total Surface Area = Lateral Surface Area + 2(Base Area)
Total Surface Area = 16956 + 2(706.5)
Total Surface Area = 16956 + 1413
Total Surface Area = 18369 square inches
Therefore, the surface area of the cylinder is 18369 square inches.