To find the surface area of a cylinder, you need to consider the formula which includes both the lateral surface area and the two circular bases.
a. First, calculate the lateral surface area:
Lateral Surface Area = 2 * π * radius * height
Substitute the values given:
Lateral Surface Area = 2 * π * 3 cm * 8 cm
Lateral Surface Area = 48π square centimeters
b. Second, find the area of the two circular bases:
Circular Base Area = π * radius^2
Substitute the radius value:
Circular Base Area = π * 3^2
Circular Base Area = 9π square centimeters
Since there are two bases, multiply this by 2:
Total Circular Base Area = 2 * 9π = 18π square centimeters
c. Finally, add the lateral surface area and the total circular base area to get the total surface area of the cylinder:
Total Surface Area = Lateral Surface Area + Total Circular Base Area
Total Surface Area = 48π + 18π
Total Surface Area = 66π square centimeters
Therefore, the surface area of the cylinder with a height of 8 centimeters and a radius of 3 centimeters is 66π square centimeters.
