Answer:
the surface area of the given cylinder is 66π square feet.
Explanation:
Given:
Base radius (r) = 3 ft
Height (h) = 8 ft
To calculate the lateral surface area of the cylinder, we use the formula:
Lateral Surface Area = 2πrh
Lateral Surface Area = 2 * π * 3 ft * 8 ft
Lateral Surface Area = 48π ft²
The base of the cylinder is a circle, and its area can be calculated using the formula:
Base Area = πr²
Base Area = π * (3 ft)²
Base Area = 9π ft²
Since the cylinder has two bases, we multiply the base area by 2 to get the total area of the bases.
Total Base Area = 2 * 9π ft²
Total Base Area = 18π ft²
To find the total surface area of the cylinder, we add the lateral surface area and the total base area:
Total Surface Area = Lateral Surface Area + Total Base Area
Total Surface Area = 48π ft² + 18π ft²
Total Surface Area = 66π ft²