Explanation:
the surface area of the cylinder is the sum of the areas of the 2 circles (bottom and top of the cylinder) and the area of the rectangle (the cut open mantle of the cylinder).
the length of the rectangle is the circumference of the top or bottom circle.
so the area of one circle is
pi×r² = 3.14×6² = 3.14×36 = 113.04 ft²
the circumference of a circle is
2×pi×r = 2×3.14×6 = 37.68 ft.
the area of the large rectangle is therefore
37.68×15.6 = 587.808 ft²
in total the surface area is
2×113.04 + 587.808 = 813.888 ft² ≈ 813.9 ft²