Final answer:
The surface area of the cylinder is calculated by finding the area of the two bases and the area of the side. The total surface area is the sum of these areas, which equals 125.60 cm² without rounding.
Step-by-step explanation:
To find the surface area of a cylinder with a height of 8 cm and a base radius of 2 cm, we need to calculate the areas of both the circular bases and the rectangular area that makes up the curved surface.
The area of one circular base is given by the formula A = πr². Since the cylinder has two bases, we multiply the area of one circle by 2:
A = 2 × π × r² = 2 × 3.14 × (2 cm)² = 2 × 3.14 × 4 cm² = 25.12 cm²
Next, we calculate the area of the side (the rectangle that wraps around the cylinder), which is the circumference of the base times the height of the cylinder:
A = 2πrh = 2 × 3.14 × 2 cm × 8 cm = 100.48 cm²
Adding both areas gives us the total surface area of the cylinder:
Total Surface Area = Area of bases + Area of side = 25.12 cm² + 100.48 cm² = 125.60 cm²
Therefore, the surface area of the cylinder is 125.60 cm² without any rounding.