Final answer:
To find the exact surface area of the cylinder, calculate the areas of the two circular bases and the lateral surface area. Substitute the given values, and use the formulas A = πr² and A = 2πrh. The exact surface area of the cylinder is 150.72 cm².
Step-by-step explanation:
To find the exact surface area of the cylinder, we need to calculate the areas of the two circular bases and the lateral surface area. The formula for the lateral surface area of a cylinder is given by A = 2πrh, where r is the radius and h is the height. Given r = 3 cm and h = 5 cm, we can substitute these values into the formula to find the lateral surface area. A = 2π(3 cm)(5 cm) = 30π cm². The formula for the area of a circle is A = πr². So, the area of each circular base is A = π(3 cm)² = 9π cm². The total surface area of the cylinder is the sum of the areas of the two circular bases and the lateral surface area: A = 2(9π cm²) + 30π cm² = 18π cm² + 30π cm² = 48π cm². Using the approximate value of π as 3.14, the exact surface area of the cylinder is 48(3.14) cm² = 150.72 cm². Therefore, the exact surface area of the cylinder is 150.72 cm².