To find the surface area of a cylinder, we need to add the areas of the top and bottom circles, which each have an area of pi times the radius squared, and the area of the curved lateral surface, which has an area of 2 times pi times the radius times the height.
So, the surface area of a cylinder with a radius of 2 feet and height of 8 feet is:
- Area of top and bottom circles: 2 x pi x r^2 = 2 x pi x (2 ft)^2 = 8 x pi ft^2
- Area of curved lateral surface: 2 x pi x r x h = 2 x pi x (2 ft) x (8 ft) = 32 x pi ft^2
Adding these areas together gives us the total surface area:
8 x pi ft^2 + 32 x pi ft^2 = 40 x pi ft^2
Therefore, the surface area of the cylinder is 40 x pi square feet, or approximately 125.66 square feet.