Answer:
In this problem, we need to find the surface area of a cylinder. Let's first identify the given information and then solve the problem step by step.
Given:
Height of the cylinder (h) = 12 yards
Circumference of the cylinder (C) = 516.18 yards
π ≈ 3.14
Step 1: Calculate the diameter (D) of the cylinder using the circumference.
C = πD
516.18 = 3.14D
D = 516.18 ÷ 3.14
D ≈ 164.39 yards
Step 2: Apply the surface area formula for a cylinder.
SA = 2πr² + 2πrh
SA = πD² + πDh
SA = 3.14 × 164.39² + 3.14 × 164.39 × 12
SA ≈ 84,853.92 + 6,188.31
SA ≈ 91,042.23 square yards
Therefore, the surface area of the cylinder is approximately 91,042.23 square yards.
